For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Madeira D, Narciso L, Cabral HN, Vinagre C, Diniz MS (2013) Influence of temperature in thermal and oxidative stress responses in estuarine fish. Comp Biochem Physiol A Mol Int Physiol 166: 237–243.

The study species shows an extremely limited geographic distribution, as it is found in a single cave in NE Spain. Beyond the interest in this particular, potentially endangered species, we seek to take advantage of the potential of subterranean environments for ecological, biogeographical and conservation research (Sánchez-Fernández et al., 2018; Mammola et al., 2019b) to both improve the understanding of the mechanisms underlying tolerance of insects to heat stress and to obtain more accurate estimates of the response of biodiversity to climate change.

Domenici P, Claireaux G, McKenzie DJ (2007) Environmental constraints upon locomotion and predator–prey interactions in aquatic organisms: an introduction. Philos Trans R Soc B Biol Sci 362: 1929–1936.

De Rosario-Martinez H (2015) Phia: post-hoc interaction analysis. R package version 0.2-1. https://CRAN.R-project.org/package=phia

Deschaseaux ES, Taylor AM, Maher WA, Davis AR (2010) Cellular responses of encapsulated gastropod embryos to multiple stressors associated with climate change. J Exp Mar Biol Ecol 383: 130–136.

Adult specimens of P. canyellesi (90 specimens approx.) were collected in Forat de las Pedreres and transported to the laboratory at cool and wet conditions in a portable fridge, using the substrate from the cave and moss to keep a high humidity (>90% RH). Sampling permits were previously approved by the corresponding local authority (Generalitat de Catalunya, permit numbers SF/994-SF/1001). In the laboratory, groups of 10 specimens were placed in different 10 × 15-cm plastic boxes with a white plaster substratum, 2–3 small volcanic stones and tissue paper (e.g. Rizzo et al., 2015; Pallarés et al., 2019). These were covered with holed plastic film to maintain RH values close to saturation but allow aeration. Containers were placed in a laboratory incubator (Radiber ERF-360, Radiber S.A., Barcelona, Spain) at the approximate temperature of the study site (13°C) and permanent dark for 2 days previous to the experiments. For the entire duration of the experiments, specimens were fed ad libitum with freshly frozen Drosophila melanogaster, and relative humidity was kept >90% by wetting the substrate, stones and papers daily and placing trays with distilled in the incubators. Temperature and relative humidities inside the containers were recorded every 5 min using HOBO MX2301 data loggers (Onset Computer Corporation, Bourne, MA, USA).

Mean ± SEM values of total antioxidant capacity (TAC), glutathione S-transferase activity (GST), ratio of reduced:oxidized forms of glutathione (GSH:GSSG), lipid peroxidation (LPO) and AChE activity. Significant differences between treatment pairs (P < 0.05 in Bonferroni post hoc tests) are represented with letters (differences between the short and long-term exposure within each temperature) or asterisks (differences between temperatures at each exposure time).

Substituting size of an Object in the field, instead of overall Field size. Using these two steps may be convenient: Object height on sensor (mm)  =   Sensor height (mm) × Object height (pixels) Sensor height (pixels) Object height on sensor (mm)Focal length (mm)  =   Real Object size *Distance to Object * Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less. Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here Copyright © 2018-2024 by Wayne Fulton - All rights are reserved.

Arribas P, Abellán P, Velasco J, Bilton DT, Millán A, Sánchez-Fernández D (2012) Evaluating drivers of vulnerability to climate change: a guide for insect conservation strategies. Glob Change Biol 18: 2135–2146.

Specimens were immediately frozen at −80°C at the end of each treatment and individually homogenized in 300 μl of ice-cold 10-mM sucrose buffer (pH = 7.4) containing 1 mM EDTA, using a plastic tissue grinder (kept on ice) and an ultrasonic cell disruptor. The homogenates were centrifuged at 10 000 × g for 5 min at 4°C, and the post-mitochondrial fraction was aliquoted and stored at −80°C until biomarker analyses. Total protein content was determined using Bradford method (Bradford, 1976) adapted to a 96-well microplate, and using bovine serum albumin as the standard.

Williams SE, Shoo LP, Isaac JL, Hoffmann AA, Langham G (2008) Towards an integrated framework for assessing the vulnerability of species to climate change. Plos Biol 6: 2621–2626.

Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Recent studies on various subterranean taxa suggest that the physiological responses underlying thermal tolerance could vary between species with different degree of specialization to the subterranean environment (e.g. Raschmanová et al., 2018; Mammola et al., 2019c). Amongst cave beetles, some deep subterranean specialist Leiodidae appear to lack thermal plasticity, like P. canyellesi, (i.e. they show no capacity for acclimation to high temperature), whilst related species less specialized to subterranean life (facultative subterranean) have some degree of acclimation capacity (Pallarés et al., unpublished data). Bernabò et al. (2011) demonstrated the occurrence of a heat shock response in two obligate subterranean leiodids, but its intensity was lower in the species confined to the internal—more thermally stable parts of caves than in its congener that lives closer to cave entrances, exposed to higher thermal fluctuations. Therefore, in the evolutionary process of specialization to the highly stable deep subterranean environments, the physiological capacity to cope with heat stress might have been reduced. The capacity to onset antioxidant responses under heat stress observed here may allow cave beetles to survive at temperatures well-above that of the habitat for a limited exposure time, as seen here and in related species (Rizzo et al., 2015). However, given the high energetic cost of such responses (Krebs and Loeschke, 1994; Tomanek, 2010), it is likely that prolonged exposure to heat stress in resource-limited environments such as caves decreases fitness in the longer time scale (Monaghan et al., 2009). Further work exploring these issues (e.g. transcriptome and proteome-level responses, metabolic rates and the fitness consequences of long-term exposure to heat stress), in species with different degrees of specialization to the subterranean environment, would contribute not only to understand the complex biochemical processes underlying heat tolerance in ectotherms, but also their evolution associated with the colonization of these extreme and stable environments.

Seebacher F, White CR, Franklin CE (2015) Physiological plasticity increases resilience of ectothermic animals to climate change. Nat Clim Change 5: 61–66.

Field of viewcamera

Habig WH, Pabst MJ, Jakoby WB (1974) Glutathione S-transferases the first enzymatic step in mercapturic acid formation. J Biol Chem 249: 7130–7139.

The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Object height on sensor (mm)  =   Sensor height (mm) × Object height (pixels) Sensor height (pixels) Object height on sensor (mm)Focal length (mm)  =   Real Object size *Distance to Object * Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less. Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here Copyright © 2018-2024 by Wayne Fulton - All rights are reserved.

Other set of specimens was exposed to the control (13°C) or high temperature (20°C) for either 2 (short-term exposure) or 7 days (long-term exposure) (n = 10 specimens per each temperature × time treatment), in order to identify potential sublethal effects of heat stress and the time dependence of the responses. The selected temperatures closely represented current and future extreme climate scenarios in the study site, respectively (see above). The short-term, 2-day exposure is a typical time point used in oxidative stress bioassays to assess the first antioxidant defence activation under stress (Saint-Denis et al., 1999; Bouchar, 2003; Colacevich et al., 2011). The 7 days of exposure was used as a longer-term exposure to relate biomarker responses with acclimation capacity, because thermal acclimation responses have been found in some subterranean invertebrates within such time (Pallarés et al., 2019 and unpublished data).

* feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Sánchez-Fernández D, Lobo JM, Hernández-Manrique OL (2011) Species distribution models that do not incorporate global data misrepresent potential distributions: a case study using Iberian diving beetles. Divers Distrib 17: 163–171.

Ellman GL, Courtney KD, Andres V Jr, Featherstone RM (1961) A new and rapid colorimetric determination of acetylcholinesterase activity. Biochem Pharmacol 7: 88–95.

Object height on sensor (mm)Focal length (mm)  =   Real Object size *Distance to Object * Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Tattersall GJ, Sinclair BJ, Withers PC, Fields PA, Seebacher F, Cooper CE, Maloney SK (2012) Coping with thermal challenges: physiological adaptations to environmental temperatures. Compr Physiol 2: 2151–2202.

Previous studies have shown that ectotherm subterranean species have narrow thermal tolerance ranges and limited acclimation capacities compared to surface-dwelling ones, some of them being extremely sensitive to thermal changes (e.g. Mermillod-Blondin et al., 2013; Di Lorenzo and Galassi, 2017; Mammola et al., 2019c). However, the upper lethal thermal limits of a number of subterranean species are well above their current habitat temperatures and those experienced through their evolutionary history (e.g. Issartel et al., 2005; Rizzo et al., 2015; Sánchez-Fernández et al., 2016; Pallarés et al., 2019). Yet, little is known about the underlying biochemical mechanisms that modulate thermal tolerance in these species as well as the physiological effects of exposure to sublethal temperatures (but see Colson-Proch et al., 2010; Bernabò et al., 2011). In this study, we combine experimental measurements of lethal thermal limits, acclimation capacity and biomarkers of oxidative stress (total antioxidant capacity, glutathione S-transferase activity, glutathione concentration and lipid peroxidation) and neurotoxicity (AChE activity) to assess the impact of heat stress on the subterranean beetle species Parvospeonomus canyellesi (Lagar, 1974) (fam. Leiodidae). We also accounted for the effect of exposure time in biomarker responses to identify transient and long-term biological adjustments to thermal stress. Some studies have shown that certain oxidative stress biomarkers (e.g. antioxidant enzyme activities) respond faster to environmental stressors than others (e.g. lipid peroxidation or DNA damage) in both vertebrates (Bouchard, 2003) and invertebrates (Colacevich et al., 2011), and the dynamic of their responses depends on the level of exposure (time × dose) to the stressors. After first short-term defence activation, an organism under thermal stress may either exhaust the cellular protection mechanisms or acclimate (Madeira et al., 2016b). Furthermore, transport and the time of maintenance of subterranean organisms in laboratory conditions may be an additional source of variation that could affect outcomes when measuring highly stress-sensitive parameters. We hypothesize that exposure to high non-lethal temperatures in subterranean insects triggers oxidative stress and locomotor impairment, consequently reducing their effective TSM under climate change, and that such effects might be time-dependent.

For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Monaghan P, Metcalfe NB, Torres R (2009) Oxidative stress as a mediator of life history trade-offs: mechanisms measurements and interpretation. Ecol Lett 12: 75–92.

Kaplan–Meir survivorship curves for each temperature treatment (13, 20, 23 and 25°C). Each data point represents survival probability (mean ± SEM).

Bouchard P (2003) Time course of the response of mitochondria from oxidative muscle during thermal acclimation of rainbow trout, Oncorhynchus mykiss. J Exp 206: 3455–3465.

Trig functions in software programming languages (including Excel, Javascript, C, Python, etc.) use radians instead of degrees. Calculators normally offer the choice of using degrees. To convert radians to degrees, multiply radians by 180/Pi, which is 57.2958 degrees per radian. Or for degrees to radians, multiply degrees by Pi/180. Field size and focal length are linear in field of view (half of sensor dimension or twice the focal length both produce half the field dimension). But the angle is a tangent function, which is Not straight-line linear (the angle is approximately linear if angle is not more than about 10 degrees (called the Small-Angle Approximation).

To determine the upper lethal temperature (ULT) of P. canyellesi, we measured survival at different temperatures, which represent its current natural conditions (13°C, used as a control treatment), and potentially sublethal (20 and 23°C) or extreme temperatures (25°C) according to the ULT reported for species of the same clade (between 20 and 23°C) (Rizzo et al., 2015). Ten specimens, placed in a plastic box were subjected to each treatment in individual climatic incubators, for 1 week. The rest of the experimental conditions were maintained as described above. Survival was monitored every 24 h. After 1-week exposure, specimens from the 13 and 20°C treatments (non-lethal temperatures) were exposed to 23°C to look at acclimation capacity (i.e. to assess whether survival under heat stress is influenced by previous thermal conditions), and survival was monitored daily until all specimens were dead (i.e. 8 days).

The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Attig H, Kamel N, Sforzini S, Dagnino A, Jamel J, Boussetta H, Viarengo A, Banni M (2014) Effects of thermal stress and nickel exposure on biomarkers responses in Mytilus galloprovincialis (Lam). Mar Environ Res 94: 65–71.

Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used.

Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Asensi M, Sastre J, Pallardo FV, Lloret A, Lehner M, Garcia-De-La Asuncion J, Viña J (1999) Ratio of reduced to oxidized glutathione as indicator of oxidative stress status and DNA damage. In Methods in Enzymology Vol 299. Academic Press, pp. 267–276.

Diamond SE, Sorger DM, Hulcr J, Pelini SL, Del Toro I, Hirsch C, Oberg E, Dunn R (2012) Who likes it hot? A global analysis of the climatic, ecological, and evolutionary determinants of warming tolerance in ants. Glob Change Biol 18: 448–456.

The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Madeira C, Mendonça V, Leal MC, Flores AA, Cabral HN, Diniz MS, Vinagre C (2018) Environmental health assessment of warming coastal ecosystems in the tropics–application of integrative physiological indices. Sci Total Environ 643: 28–39.

Kellermann V, van Heerwaarden B (2019) Terrestrial insects and climate change: adaptive responses in key traits. Physiol Entomol 44: 99–115.

Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Lauritzen SE (2018) Physiography of the caves. In OT Moldovan, L Kovác, S Halse, eds, Cave Ecology. Springer, Cham, pp. 7–22

Sanchez W, Burgeot T, Porcher JM (2013) A novel “integrated biomarker response” calculation based on reference deviation concept. Environ Sci Pollut Res 20: 2721–2725.

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We are very grateful to Ignacio Ribera for providing valuable suggestions at different stages of this manuscript. We also thank Stefano Mammola and an anonymous reviewer for a very constructive revision of the manuscript.

This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Accurate assessments of species vulnerability to climate change need to consider the physiological capacity of organisms to deal with temperature changes and identify early signs of thermally induced stress. Oxidative stress biomarkers and acetylcholinesterase activity are useful proxies of stress at the cellular and nervous system level. Such responses are especially relevant for poor dispersal organisms with limited capacity for behavioural thermoregulation, like deep subterranean species. We combined experimental measurements of upper lethal thermal limits, acclimation capacity and biomarkers of oxidative stress and neurotoxicity to assess the impact of heat stress (20°C) at different exposure times (2 and 7 days) on the Iberian endemic subterranean beetle Parvospeonomus canyellesi. Survival response (7 days of exposure) was similar to that reported for other subterranean specialist beetles (high survival up to 20°C but no above 23°C). However, a low physiological plasticity (i.e. incapacity to increase heat tolerance via acclimation) and signs of impairment at the cellular and nervous system level were observed after 7 days of exposure at 20°C. Such sublethal effects were identified by significant differences in total antioxidant capacity, glutathione S-transferase activity, the ratio of reduced to oxidized forms of glutathione and acetylcholinesterase activity between the control (cave temperature) and 20°C treatment. At 2 days of exposure, most biomarker values indicated some degree of oxidative stress in both the control and high-temperature treatment, likely reflecting an initial altered physiological status associated to factors other than temperature. Considering these integrated responses and the predicted increase in temperature in its unique locality, P. canyellesi would have a narrower thermal safety margin to face climate change than that obtained considering only survival experiments. Our results highlight the importance of exploring thermally sensitive processes at different levels of biological organization to obtain more accurate estimates of the species capacity to face climate change.

Campos DF, Braz-Mota S, Val AL, Almeida-Val VMF (2019) Predicting thermal sensitivity of three Amazon fishes exposed to climate change scenarios. Ecol Indic 101: 533–540.

CCTVfield of viewcalculator

Somero GN (2010) The physiology of climate change: how potentials for acclimatization and genetic adaptation will determine ‘winners’ and ‘losers’. J Exp Biol 213: 912–920.

1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Sará G, Kearney M, Helmuth B (2011) Combining heat-transfer and energy budget models to predict thermal stress in Mediterranean intertidal mussels. Chem Ecol 27: 135–145.

Species vulnerability to climate change depends on the capacity of individuals to maintain current populations or to shift geographical ranges to future suitable environments (Williams et al., 2008). These processes are ultimately related to the niche breadth (Kearney, 2006) and dispersal capacity. However, most studies forecasting species responses to climate change do not account for their actual environmental tolerances, as relevant physiological traits are not explicitly considered (Kearney et al., 2010). Experimental measurements of such traits, as proxies of the species’ fundamental niche breadth (sensuHutchinson, 1957), have the potential to improve species vulnerability assessments (Somero, 2010; Arribas et al., 2012).

Chown SL (2012) Trait-based approaches to conservation physiology: forecasting environmental change risks from the bottom up. Philos Trans R Soc B Biol Sci 367: 1615–1627.

Evans TG, Diamond SE, Kelly MW (2015) Mechanistic species distribution modelling as a link between physiology and conservation. Cons Physiol 3: cov056.

Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

* feet or meters (but both same units) Meaning, if you use Feet for Distance, then the Field Width will also be feet. Or meters if you use meters. Rearrange ratios to compute desired unknown value. The actual Field of View Calculator will be much more versatile, and can help find sensor size from crop factor, but math examples are shown here for Width. The computed Dimension can be Width, Height, or Diagonal. Sensor Width mm × Distance Focal Length mm  = Field Width   Field Width × Focal Length mm Sensor Width mm  = Distance    This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

Rane RV, Ghodke AB, Hoffmann AA, Edwards OR, Walsh TK, Oakeshott JG (2019) Detoxifying enzyme complements and host use phenotypes in 160 insect species. Curr Opin Insect Sci 31: 131–138.

The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Engenheiro EL, Hankard PK, Sousa JP, Lemos MF, Weeks JM, Soares AM (2005) Influence of dimethoate on acetylcholinesterase activity and locomotor function in terrestrial isopods. Environ Toxicol Chem 24: 603–609.

In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting.

Response of AChE activity indicated heat-induced stress also at the nervous system at the long-term, as the activity of this enzyme was higher at 20 than 13°C at 7 days. Such increase of AChE activity may reflect higher locomotor activity under high temperature (e.g. Kjærsgaard et al., 2010). Indeed, previous studies have found a positive correlation between AChE activity and locomotor behaviour parameters in invertebrates (e.g. Engenheiro et al., 2005; Xuereb et al., 2009), showing the significant physiological role of this esterase in animal locomotion activity. Although locomotor parameters were not systematically registered in our experiment, we observed that specimens were generally much more active in the 20°C treatment, supporting such hypothesis. However, such up-regulation of AChE under thermal stress contrasts with other studies, which have shown the opposite pattern (i.e. an inhibition of AChE activity) (e.g. Scaps and Borot, 2000; Dimitriadis et al., 2012; Attig et al., 2014). It could not be discarded that a more prolonged exposure or higher temperatures would down-regulate the AChE activity in P. canyellesi.

To assess the impact of temperature on the biomarkers measured at short- (2 days) and long-term exposure (7 days), we used the integrated biomarker response (IBR) index, the IBRv2, which is a modified version by Sanchez et al. (2013) of the original IBR index (Beliaeff and Burgeot, 2002). The index integrates the response of multiple biomarkers to provide a measurement of the organism’ physiological status at specific environmental conditions. Star-plots of the Ai-score outcome (individual biomarker deviation index) obtained from IBR calculation allowed the visual assessment of the response (inhibition or induction) of each biomarker (seeSupplementary Material, Appendix S2). The specific responses of individual biomarkers to temperature and exposure time were also explored by performing a two-way ANOVA test for each biomarker, including temperature, time and their interaction as predictors. When significant effects were detected, pairwise post hoc tests with Bonferroni correction were used to compare biomarker values between treatments.

Colacevich A, Sierra MJ, Borghini F, Millán R, Sanchez-Hernandez JC (2011) Oxidative stress in earthworms short- and long-term exposed to highly Hg-contaminated soils. J Hazard Mater 194: 135–143.

This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

IBRv2 values were 1.04 and 4.40 for 2 and 7 days of exposure, respectively, showing a higher impact of temperature on biomarker responses at longer than short-term exposure. The star plots of the Ai-scores evidenced an increase of TAC and GST activity at both exposure times, as well as an increase of AChE activity and a marked and slight decrease in the GSH:GSSG ratio and LPO, respectively, at longer-term exposure (Fig. 2).

Kellermann V, Overgaard J, Hoffmann AA, Flojgaard C, Svenning JC, Loeschcke V (2012) Upper thermal limits of Drosophila are linked to species distributions and strongly constrained phylogenetically. P Natl Acad Sci USA 109: 16228–16233.

The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Mammola S, Piano E, Cardoso P, Vernon P, Domínguez-Villar D, Culver DC, Pipan T, Isaia M (2019b) Climate change going deep: the effects of global climatic alterations on cave ecosystems. Anthr Rev 6: 98–116. doi: 10.1177/2053019619851594.

van der Oost R, Beyer J, Vermeulen NPE (2003) Fish bioaccumulation and biomarkers in environmental risk assessment: a review. Environ Toxicol Pharmacol 13: 57–149.

This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

R Core Team (2019) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, https://www.R-project.org/

All analyses were performed in R v.3.3.3. (R Core Team, 2019) using the packages 'survival' (Therneau, 2015), 'survminer' (Kassambara et al., 2019), 'MASS' (Venables and Ripley, 2002) and 'phia' (De Rosario-Martinez, 2015).

Sensor Width mm × Distance Focal Length mm  = Field Width   Field Width × Focal Length mm Sensor Width mm  = Distance    This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent.

There are approximations in calculations. The math is precise, but the data is less so. The required Focal length and Sensor Size are rounded specifications, losing a bit of precision. This little difference at the small sensor gets magnified in the field and scene. However, the results certainly are close enough to be very useful in any practical case. My experience is that the field is fairly accurate (at distances of at least a meter or so), assuming you actually know your parameters. Some problems are: You absolutely must know the actual correct sensor size in mm. Or the FOV calculator here can make a reasonable approximation of sensor size from the accurate Crop Factor. If not accurate, the field of view calculation will not be accurate. If you're guessing, your results will likely be troubled. Please see this summary of Issues determining Sensor Size which might help. You must know the actual correct lens focal length in mm. Zoom lens focal length is different at each and every zoom position. The image EXIF data may show focal length (but it is rounded in some degree). And of course just guessing about the field distance may be an approximation, or may not be at all accurate. Field of View calculators do NOT work for macro distances. Macro uses reproduction ration, like 1:1. Thin Lens Equation The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting. Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Field of viewcalculator astrophotography

Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

FOV to focal length calculator

S.P, D.S-F and J.C.S-H conceived the idea and designed the experiments, P.B-G and J.C. collected the specimens, S.P., J.C.S-H and R.C. performed the experiments and S.P. analysed the data and led the manuscript writing. All authors discussed the idea and results, contributed to the manuscript drafts and gave final approval for publication.

Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Domingues I, Agra AR, Monaghan K, Soares AMVM, Nogueira AJA (2010) Cholinesterase and glutathione-S-transferase activities in freshwater invertebrates as biomarkers to assess pesticide contamination. Environ Toxicol Chem 29: 5–18.

Sánchez-Fernández D, Rizzo V, Cieslak A, Faille A, Fresneda J, Ribera I (2016) Thermal niche estimators and the capability of poor dispersal species to cope with climate change. Sci Rep 6: 23381. doi: 10.1038/srep23381.

Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Dimitriadis VK, Gougoula C, Anestis A, Pörtner HO, Michaelidis B (2012) Monitoring the biochemical and cellular responses of marine bivalves during thermal stress by using biomarkers. Mar Environ Res 73: 70–77.

Despite the fact that the fragility of the subterranean world is widely recognized (Reboleira et al., 2011; Mammola et al., 2019a), subterranean habitats and species remain largely neglected in conservation programmes. Thus, it is time to go a step forward into the effective protection of this unique and valuable component of biodiversity. The identification and protection of areas with high values of subterranean biodiversity and the application of conservation measures to minimise the threats affecting it must be a priority.

P. canyellesi did not show an enhancement of heat resistance after previous acclimation at 20°C during 7 days. In agreement with such acclimation failure, biomarker responses revealed sublethal effects of high temperature exposure, of much greater magnitude at long than short-term exposure (4-fold higher IBR v2 values). High IBRv2 values, reflecting altered physiological status, have been associated with low acclimation abilities (Madeira et al., 2016, 2018; Campos et al., 2019). Specifically, after 7 days of incubation, the significant increase of TAC and GST activity in parallel with the decrease of GSH:GSSG ratio in the 20°C treatment, compared to controls, suggest activation of both molecular and enzymatic antioxidant mechanisms. Despite the lack of acclimation capacity of the species, such antioxidant response appeared to be effective in controlling irreversible damage to membranes, since LPO levels did not differ between the control and stressful treatment at this exposure time. It has been long reported that exposure to chemical stressors, such as environmental contaminants, cause an imbalance in the cellular oxidative status that lead to a decreased GSH:GSSG ratio and activation of GSH, amongst other enzymatic antioxidant mechanisms (Storey, 1996; Asensi et al., 1999; Amaral et al., 2012). Therefore, our findings suggest a quick response of glutathione-dependent antioxidant mechanisms against heat stress; the sensitivity and magnitude of such response could be critical for the adaptation potential of the study species to global warming. Whether this response is similar in other subterranean species remains to be investigated, as glutathione metabolism appears to be highly species-specific (Enayati et al., 2005; Domingues et al., 2010; Rane et al., 2019).

Beliaeff B, Burgeot T (2002) Integrated biomarker response: a useful tool for ecological risk assessment. Environ Toxicol Chem 21: 1316–1322.

Baldwin J (1971) Adaptation of enzymes to temperature: acetylcholinesterases in the central nervous system of fishes. Comp Biochem Physiol B Comp Biochem 40: 181–187.

The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting.

But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Bernabò P, Latella L, Jousson O, Lencioni V (2011) Cold stenothermal cave-dwelling beetles do have an HSP70 heat shock response. J Therm Biol 36: 206–208.

Rahman I, Kode A, Biswas SK (2006) Assay for quantitative determination of glutathione and glutathione disulfide levels using enzymatic recycling method. Nat Protoc 1: 3159.

Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Scaps P, Borot O (2000) Acetylcholinesterase activity of the polychaete Nereis diversicolor: effects of temperature and salinity. Comp Biochem Physiol C Parmacol Toxicol Endocrinol 125: 377–383.

The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Fresneda X, Salgado JM (2016) Catálogo de los Coleópteros Leiodidae Cholevinae Kirby, 1837 de la península Ibérica e islas Baleares. Monografies del Museu de Ciències Naturals de Barcelona 7: 1–308.

Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Thin Lens Equation The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting. Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Enzor LA, Place SP (2014) Is warmer better? Decreased oxidative damage in notothenioid fish after long-term acclimation to multiple stressors. J Exp Biol 217: 3301–3310.

Goh BPL, Lai CH (2014) Establishing the thermal threshold of the tropical mussel Perna viridis in the face of global warming. Mar Pollut Bull 85: 325–331.

Many molecular and biochemical mechanisms are triggered under thermal stress in ectotherms (Tattersall et al., 2012). Amongst them, high temperature stress increases the production of cellular reactive oxygen species (ROS), leading to oxidative stress (Tomanek, 2015). Oxidative stress is defined as an imbalance of oxidant molecules and antioxidant mechanisms in favour of the former, which leads to disruption of redox signalling and control as well as biomolecule damage (Sies and Jones, 2007). The organism has evolved complex molecular and enzymatic defence systems against excessive ROS production to maintain the cellular redox homeostasis. It is generally assumed that a limited antioxidant capacity leads to poor acclimation potential (Madeira et al., 2018), and ultimately, limited health status and low capacity to cope with environmental stressors (e.g. Yang et al., 2010; Madeira et al., 2013; Enzor and Place, 2014). Thermal stress has also a significant impact on locomotion, an energetically costly trait and major component in the individual fitness and organisms’ ability to cope with different environments (Domenici et al., 2007). In locomotion, cholinergic synapses are essential in the neuromuscular transmission, and the enzyme acetylcholinesterase (AChE, EC 3.1.1.7) plays a pivotal role in the regulation of the nervous impulse via hydrolysis of the neurotransmitter acetylcholine. This highly temperature-sensitive enzyme (Baldwin, 1971; Scaps and Borot, 2000; Pfeifer et al., 2005; Dimitriadis et al., 2012; Attig et al., 2014) can be used as an indicator of physiological stress at the nervous system level. Together with oxidative stress parameters, it provides a potentially useful biomarker to identify early signs of thermal stress and altered metabolic processes. Such estimates may help to interpret outcomes from survival experiments in thermal stress research and to refine assessments of species vulnerability to climate change (e.g. Deschaseaux et al., 2010; Goh and Lai, 2014; Madeira et al., 2016; Campos et al., 2019).

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

Parvospeonomus canyellesi is a troglobiont (i.e. obligate subterranean) species endemic to Spain and cited in a single cave ('Forat de las Pedreres') (Fresneda and Salgado, 2016). This cave is located in a mining area in the Montseny mountainous massif, a Catalan pre-coastal mountain range designated as Natural Park and UNESCO Biosphere Reserve. The species is neither considered of conservation concern nor has any national or international legal protection despite of its extremely reduced geographical distribution and high habitat specialization. It shows several traits associated with the subterranean specialization in Leptodirini beetles, e.g. complete loss of eyes, elongated appendages and a modified life cycle with two larval instars, observed only in strictly subterranean species and different from the three-instar cycle typical in most Coleoptera (Cieslak et al., 2014a, b; Ribera et al., 2018). However, it does not exhibit other extreme modifications observed in related species specialized in deep subterranean habitats (e.g. increased body size and the most modified life cycle with a single larval instar), which may suggest an intermediate degree of subterranean specialization for this species.

Reboleira AS, Borges PAV, Gonçalves F, Serrano A, Oromí P (2011) The subterranean fauna of a biodiversity hotspot region - Portugal: an overview and its conservation. Int J Speleol 40: 23–37.

On the other hand, high and low LPO and GSH:GSSG ratio values, respectively, indicated some signs of oxidative stress in both the control and heat treatment at 2 days, if such values are compared with those at 7 days. Oxidative stress in specimens exposed to a temperature that is a priori not stressful (i.e. the control temperature in this study), and its subsequent recovery after longer exposure time, might reflect an initial altered physiological status associated to factors other than temperature, likely as a consequence of the recent collection, transport and handling in the laboratory. This side effect may have important implications from a methodological point of view. When using field-collected specimens for experiments, exposure time should be set so that specimens can recover from any stress associated to collection and transport but also avoiding stress caused by long-term holding at laboratory, non-natural conditions. In the light of our results, controlling for these potentially confounding effects is especially critical for species inhabiting highly stable habitats such as subterranean environments.

Tomanek L (2010) Variation in the heat shock response and its implication for predicting the effect of global climate change on species’ biogeographical distribution ranges and metabolic costs. J Exp Biol 213: 971–979.

Jiménez-Valverde A, Lobo JM, Hortal J (2008) Not as good as they seem: the importance of concepts in species distribution modelling. Divers Distrib 14: 885–890.

Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Agarwal R, Chase SD (2002) Rapid, fluorimetric-liquid chromatographic determination of malondialdehyde in biological samples. J Chromatogr B 775: 121–126.

Rizzo V, Sánchez-Fernández D, Fresneda J, Cieslak A, Ribera I (2015) Lack of evolutionary adjustment to ambient temperature in highly specialized cave beetles. BMC Evol Biol 15: 10.

There is a Field of View Calculator here, but this page is about the math. There are approximations in calculations. The math is precise, but the data is less so. The required Focal length and Sensor Size are rounded specifications, losing a bit of precision. This little difference at the small sensor gets magnified in the field and scene. However, the results certainly are close enough to be very useful in any practical case. My experience is that the field is fairly accurate (at distances of at least a meter or so), assuming you actually know your parameters. Some problems are: You absolutely must know the actual correct sensor size in mm. Or the FOV calculator here can make a reasonable approximation of sensor size from the accurate Crop Factor. If not accurate, the field of view calculation will not be accurate. If you're guessing, your results will likely be troubled. Please see this summary of Issues determining Sensor Size which might help. You must know the actual correct lens focal length in mm. Zoom lens focal length is different at each and every zoom position. The image EXIF data may show focal length (but it is rounded in some degree). And of course just guessing about the field distance may be an approximation, or may not be at all accurate. Field of View calculators do NOT work for macro distances. Macro uses reproduction ration, like 1:1. Thin Lens Equation The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting. Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

It is well-established that biomarker responses are time-dependent (Madeira et al., 2016). After a first defence activation, antioxidant biomarkers may decrease reflecting either exhausted responses or acclimation. We observed here that the cellular defence against thermal stress was not yet onset at 2 days of exposure, as no significant effect of temperature was found for any biomarker. At 7 days of exposure, antioxidant mechanisms were active and not exhausted, but were not effective in allowing thermal acclimation (as mentioned above).

Kearney MR, Wintle BA, Porter WP (2010) Correlative and mechanistic models of species distribution provide congruent forecasts under climate change. Conserv Lett 3: 203–213.

Temperature had a significant effect on survival time (log-rank test: χ2 = 47.6, df = 3, P < 0.001). Most of the specimens survived 7 days after exposure to both 13 and 20°C (Bonferroni-adjusted P = 0.31, df = 1). Survival times in the 23 and 25°C treatments were significantly different from the other treatments (all Bonferroni-adjusted Ps < 0.001, df = 1). Exposure to 23°C caused a progressive decrease of animal survival, which led to 100% mortality at the end of the survival experiment. No specimens survived longer than 1 day at 25°C (Fig. 1). The estimated LT50 at 7 days was 21.13 ± 0.49°C.

Sánchez-Fernández D, Aragón P, Bilton DT, Lobo JM (2012) Assessing the congruence of thermal niche estimations derived from distribution and physiological data. A test using diving beetles. Plos ONE 7: e48163.

Madeira C, Madeira D, Diniz MS, Cabral HN, Vinagre C (2016) Thermal acclimation in clownfish: an integrated biomarker response and multi-tissue experimental approach. Ecol Indic 71: 280–292.

This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

Adult specimens of P. canyellesi showed similar heat tolerance in the survival experiment than other species of the same clade, whose ULT were measured under the same approach (i.e. no survival above 23°C after 7 days of exposure) (Rizzo et al., 2015). This species can withstand temperatures much higher (around >6°C) than that of its habitat, which is also in agreement with other studies of heat tolerance in several subterranean taxa (e.g. Issartel et al., 2005; Mermillod-Blondin et al., 2013; Rizzo et al., 2015; Pallarés et al., 2019). However, acclimation and biomarker experiments indicated that P. canyellesi might have difficulties in coping with rising temperature due to a combination of low physiological plasticity and signs of heat-induced impairment at the cellular and nervous system level.

Susana Pallarés, Juan C Sanchez-Hernandez, Raquel Colado, Pau Balart-García, Jordi Comas, David Sánchez-Fernández, Beyond survival experiments: using biomarkers of oxidative stress and neurotoxicity to assess vulnerability of subterranean fauna to climate change, Conservation Physiology, Volume 8, Issue 1, 2020, coaa067, https://doi.org/10.1093/conphys/coaa067

Calculate field of viewmicroscope

Amongst the multiple dimensions of species niches, the 'thermal niche' (i.e. the range of body temperatures maintaining positive population growth; Gvoždík, 2018) is key for small ectotherms, as ambient temperature affects most aspects of individual performance and fitness (Chown and Nicolson, 2004; Chown et al., 2004; Chown, 2012; Gonzalez-Tokman et al., 2020). Some studies have combined climatic and experimental data to calculate thermal safety margins (TSM), i.e. the difference between habitat temperature and the species’ critical thermal maxima (CTmax) (e.g. Diamond et al., 2012; Kellermann et al., 2012; Kellermann and van Heerwaarden, 2019). Such CTmax are typically estimated from survival experiments and assumed to be reliable proxies for the species’ capacity to deal with warming. However, thermal sensitivity often occurs in a hierarchical manner, such that processes most sensitive to environmental change can limit the overall fitness of an organism, and survival is often possible over a wider range of temperatures than locomotion, development or reproduction (Buckley and Kingsolver, 2012; Evans et al., 2015). Otherwise, capacity for thermal acclimation may extend critical limits for performance or survival (Seebacher et al., 2015).

Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Erel O (2004) A novel automated direct measurement method for total antioxidant capacity using a new generation, more stable ABTS radical cation. Clin Biochem 37: 277–285.

Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Altman DG (1992) Analysis of survival times. In DG Altman, ed, Practical Statistics for Medical Research. Chapman and Hall, London, pp. 365–393

Enayati AA, Ranson H, Hemingway J (2005) Insect glutathione transferases and insecticide resistance. Insect Mol Biol 14: 3–8.

Mermillod-Blondin F, Lefour C, Lalouette L, Renault D, Malard F, Simon L, Douady CJ (2013) Thermal tolerance breadths among groundwater crustaceans living in a thermally constant environment. J Exp Biol 216: 1683–1694.

These results stress the need of exploring thermally sensitive processes at different levels of biological organization, beyond typical survival experiments. This approach would allow to obtain more accurate estimates of the capability of poor dispersal species to cope with temperatures outside those they currently experience, and consequently, better estimates of species capacity to face climate change.

Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

According to our survival experiments, the studied cave-adapted species would have a relatively wide TSM to cope with the predicted temperature increase in its current (and unique) locality (a difference of ca. 3.5–5.6°C between the future predicted temperature at its locality under a pessimistic and optimistic scenario, respectively, and the estimated LT50 values). However, by combining survival, acclimation and molecular stress biomarkers, we showed that exposure at temperatures below lethal limits induced oxidative stress and alteration of the activity of a key nervous system enzyme (AChE), and prevented acclimation under a subsequent thermal challenge. Long-term persistence of an organism in a given location is more likely to be defined by thermal constraints on physiological performance than thresholds for heat-induced mortality (Sará et al., 2011; Evans et al., 2015). Therefore, in the basis of our results, persistence of P. canyellesi in a scenario of maintained temperatures close to its lethal limit could not be guaranteed. For most taxa, ULTs or other CTmax are frequently the only physiological end point available (or the easiest to measure) to estimate TSM in assessments of vulnerability to climate change. For example, Sánchez-Fernández et al. (2016) predicted that species of a lineage of Leptodirni beetles will have suitable habitat conditions (i.e. wide TSM) under climate change scenarios considering experimental data on thermal limits for survival, which was a more optimistic prediction than that obtained with other approaches (bioclimatic models). However, results in our study suggest that such forecasts should be also taken with caution, as they might overestimate the actual sensitivity to thermal stress. Further work exploring the responses of these biomarkers within a range of temperatures between 13 and 20°C would allow to estimate the exact threshold temperature that onsets cellular and biochemical alterations and get more biologically relevant TSM for the study species. It is also noteworthy that longer exposure times would be needed to detect effects of temperature in longer-term processes, and that measurements on other traits such as fecundity, or on other life-cycle stages, might reduce even more the thermal window for species persistence.

Temperature in the deep parts of caves is relatively constant through the day and year (Badino, 2010; Mammola & Isaia, 2016), and it can be indirectly estimated from the mean annual temperature of the surface, as both values are highly correlated (Poulson and White, 1969; Badino, 2004; Mammola et al., 2017; Sánchez-Fernández et al., 2018). Accordingly, we obtained the current surface mean annual temperature at the study site from the WorldClim database (WorldClim v.1.4; http://www.worldclim.org). We also obtained the predicted mean annual temperature for future climatic scenarios (2070) under the most optimistic (2.6) and pessimistic (8.5) representative concentration pathway (RCP). We averaged the estimates from all the general circulation models available in WorldClim for each RCP, to account for the uncertainty associated to different models. Both current and future temperatures were obtained at 30-arc-second spatial resolution. The current surface annual temperature at the cave location is 13.7°C, and it is predicted to increase up to 15.5 (RCP 2.6) or 17.4°C (RCP 8.5) by 2070.

However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

FOV to mm calculator

Issartel J, Hervant F, Voituron Y, Renault D, Vernon P (2005) Behavioural, ventilatory and respiratory responses of epigean and hypogean crustaceans to different temperatures. Comp Biochem Physiol A Mol Int Physiol 141: 1–7.

Field size and focal length are linear in field of view (half of sensor dimension or twice the focal length both produce half the field dimension). But the angle is a tangent function, which is Not straight-line linear (the angle is approximately linear if angle is not more than about 10 degrees (called the Small-Angle Approximation).

Camerafield of viewsimulator

Mammola S, Piano E, Malard F, Vernon P, Isaia M (2019c) Extending Janzen’s hypothesis to temperate regions: a test using subterranean ecosystems. Funct Ecol 33: 1638–1650.

We measured the following biomarkers of oxidative stress: the total antioxidant capacity (TAC), glutathione S-transferase activity (GST, EC 2.5.1.18), concentration of reduced (GSH) and oxidized (GSSG) forms of glutathione and lipid peroxidation (LPO). TAC is a global measure of the antioxidant compounds present in the sample. This biomarker was measured following the protocol by Erel (2004). GST activity participates not only in the metabolism of xenobiotic compounds (van der Oost et al., 2003), but also in the ROS inactivation (Hayes et al., 2005). It was measured by the method described by Habig et al. (1974). Glutathione is a tripeptide highly reactive against ROS (van der Oost et al., 2003). Its oxidation by ROS contributes to reduce the cellular oxidative stress, so a decrease in the GSH:GSSG ratio is commonly considered as an indicator of oxidative stress (Storey, 1996; Asensi et al., 1999; Amaral et al., 2012). GSH and GSSG concentrations were measured following the method by Rahman et al. (2006). LPO was measured as an indicator of oxidative damage because it is the result of the interaction between ROS and polyunsaturated fatty acids, leading to severe injury of plasma membranes (Halliwell and Chirico, 1993; Halliwell and Gutteridge, 1999). LPO was estimated by the formation of thiobarbituric acid reactive substances (TBARs) according to the method by Agarwal and Chase (2002). We also measured AChE activity as a biomarker of stress at the nervous system level, according to the method by Ellman et al. (1961). Detailed information of the protocols used to measure each parameter is provided as Supplementary Material (Appendix S1).

This work was supported by the Agencia Estatal de Investigación (Spain), the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund [project CGL2016-76995-P]. S.P. is funded by a postdoctoral grant from Fundación Seneca - Agencia de Ciencia y Tecnología de la Región de Murcia (Spain), D.S-F is funded by a postdoctoral grant from the University of Murcia (Spain) and R.C. and P.B-G are funded by predoctoral grants from the Spanish Ministry of Science, Innovation and Universities.

Specimens acclimated at 13 and 20°C and subsequently exposed at 23°C had a mean survival time of 6.3 ± 0.37 days (n = 10) and 6.75 ± 0.25 days (n = 8), respectively. No significant differences between treatments were found (log-rank test: χ2 = 0.4, df = 1, P = 0.5), indicating no acclimation capacity.

Bradford MM (1976) A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding. Anal Biochem 72: 248–254.

Di Lorenzo T, Galassi DMP (2017) Effect of temperature rising on the stygobitic crustacean species Diacyclops belgicus: does global warming affect groundwater populations? Water 9: 951. doi: 10.3390/w9120951.

Field Width × Focal Length mm Sensor Width mm  = Distance    This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

Chown SL, Gaston KJ, Robinson D (2004) Macrophysiology: large-scale patterns in physiological traits and their ecological implications. Func Ecol 18: 159–167.

Krebs RA, Loeschcke V (1994) Costs and benefits of activation of the heat-shock response in Drosophila melanogaster. Funct Ecol 8: 730–737.

Kjærsgaard A, Demontis D, Kristensen TN, Le N, Faurby S, Pertoldi C, Sorensen JG, Loeschcke V (2010) Locomotor activity of Drosophila melanogaster in high temperature environments: plastic and evolutionary responses. Clim Res 43: 127–134.

Star plots associated to the IBRv2 index, showing Ai-scores (deviation indexes) for total antioxidant capacity (TAC), glutathione S-transferase activity (GST), ratio of reduced:oxidized forms of glutathione (GSH:GSSG), lipid peroxidation (LPO) and AChE activity at (a) 2 days and (b) 7 days of exposure to contrasting temperatures. Dashed lines represent the reference treatment (control group at 13°C), and the red polygon represents the 20°C treatment. See Supplementary Material (Appendix S2) for details on index calculations.

Individually, most biomarkers (GST, GSH:GSSG ratio and AChE) showed a time-dependent response to temperature (significant interaction temperature × time, see Supplementary Material, Table S1). TAC increased with both temperature and exposure time (Fig. 2a, Table S1). GST and AChE activity increased with temperature, but such effect was only significant after 7 days of incubation (Fig. 2b and e, Table S1). The GSH:GSSG ratio was significantly lower at short- than long-term exposure, and at 7 days, it was lower at 20°C than 13°C (Fig. 3c, Table S1). TBAR levels were lower at short than long-term exposure, but not significantly affected by temperature at any exposure time (Fig. 2d, Table S1).

Colson-Proch C, Morales A, Hervant F, Konecny L, Moulin C, Douady CJ (2010) First cellular approach of the effects of global warming on groundwater organisms: a study of the HSP70 gene expression. Cell Stress Chaperon 15: 259–270.

1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

One of the main limitations for predicting species responses to climate change is the difficulty to account for species dispersal capacity and the ability to buffer from stressful temperatures by behavioural adjustments (Jiménez-Valverde et al., 2008; Sánchez-Fernández et al., 2011, 2012). Exceptionally, such limitations inherent to most environments are minimized in deep subterranean habitats (Sánchez-Fernández et al., 2012, 2018). These habitats are characterized by extremely reduced environmental variability across both time and space (Lauritzen, 2018); so, deep subterranean organisms have a limited behavioural capacity to exploit different microhabitats compared to most surface-dwelling species. Furthermore, these species are generally poor dispersers, usually with restricted ranges and isolated populations (Culver and Pipan, 2019; Ribera et al., 2018). This means that their fate under climate change will depend almost entirely on their physiological thermal tolerance and the capacity to persist in their current locations, which somehow simplifies vulnerability assessments, but places subterranean fauna as a potentially highly endangered component of global biodiversity (Sánchez-Fernández et al., 2016, Mammola et al., 2019a,b). Accordingly, experimental estimates on the temperature effects at the physiological level and on individual performance are essential if we aim to get accurate predictions on the impact of global warming in subterranean fauna.

However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Culver DC, Pipan T (2019) The Biology of Caves and Other Subterranean Habitats, Ed2nd. Oxford University Press, Oxford.

Pallarés S, Colado R, Pérez-Fernández T, Wesener T, Ribera I, Sánchez-Fernández D (2019) Heat tolerance and acclimation capacity in subterranean arthropods living under common and stable thermal conditions. Ecol Evol 9: 13731–13739.

This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Cieslak A, Fresneda J, Ribera I (2014b) Life-history specialization was not an evolutionary dead-end in Pyrenean cave beetles. Proc R Soc B 281: 20132978.

But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent.

Hikvisionfield of viewcalculator

Kassambara A, Kosinski M, Biecek P (2019) survminer: drawing survival curves using 'ggplot2'. R package version 0.4.6. https://CRAN.R-project.org/package=survminer

Halliwell B, Chirico S (1993) Lipid peroxidation: its mechanism, measurement, and significance. Am J Clin Nutr 57: 715S–725S.

Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Therneau T (2015) A package for survival analysis in S. version 2.38, 2nd September 2018.

Buckley LB, Kingsolver JG (2012) Functional and phylogenetic approaches to forecasting species’ responses to climate change. Annu Rev Ecol Evol Syst 43: 205–226.

The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Xuereb B, Lefèvre E, Garric J, Geffard O (2009) Acetylcholinesterase activity in Gammarus fossarum (Crustacea: Amphipoda): linking AChE inhibition and behavioural alteration. Aquat Toxicol 94:114±22.

Amaral MJ, Bicho RC, Carretero MA, Sanchez-Hernandez JC, Faustino AM, Soares AM, Mann RM (2012) The use of a lacertid lizard as a model for reptile ecotoxicology studies: part 2–biomarkers of exposure and toxicity among pesticide exposed lizards. Chemosphere 87: 765–774.

Ribera I, Cieslak A, Faille A, Fresneda J (2018) Historical and ecological factors determining cave diversity. In OT Moldovan, L Kovác, S Halse, eds, Cave ecology, Cham, pp. 229–252.

González-Tokman D, Córdoba-Aguilar A, Dáttilo W, Lira-Noriega A, Sánchez-Guillén RA, Villalobos F (2020) Insect responses to heat: physiological mechanisms, evolution and ecological implications in a warming world. Biol Rev . doi: 10.1111/brv.12588.

This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

We used Kaplan–Meier survivorship curves (Altman, 1992) for a visual comparison of survival at the different tested temperatures. Right censored data were specified for those individuals that were alive at the end of the 7 days of exposure (see Therneau, 2015). The overall effect of treatment on survival time was assessed by a log-rank test (Harrington & Fleming, 1982). Differences amongst treatments were determined by pairwise comparisons using also log-rank tests with Bonferroni-adjusted P values. The same procedure was used to determine acclimation capacity, i.e. to determine the effect of acclimation temperature (13 vs. 20°C) on survival time under the subsequent exposure to 23°C. To estimate ULTs, survival data at the end of the 7 days of exposure at 13–25 °C were fitted to a logistic regression model from which LT50 values (median lethal temperature, i.e. the temperature at which 50% of the exposed individuals have died) were obtained.

Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.