Shanghai Optics custom microscope objectives are designed with the assistance of CAD, Solidworks and Zemax software using top quality glass having highly specific refractive indices. This enables us to produce microscope objectives that are very low in dispersion and corrected for the most of the common optical artifacts such as coma, astigmatism, geometrical distortion, field curvature, spherical and chromatic aberration.

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.

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

Finite-corrected objectives are always designed for a certain tube length, e.g. according to DIN or JIS standard (which differ by 10 mm in tube length). Using an objective of the wrong standard may significantly deteriorate the obtained image quality.

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

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

Some microscopes allow the injection of illumination light through the objective to the sample. It is then important that there is no significant scattering of light in the objective.

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.

Microscopeparts

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)

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.

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)

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Particularly for objectives with high numerical aperture, a high image quality can be achieved only with substantial efforts for correcting various kinds of optical aberrations such as spherical, astigmatism, coma, field curvature, image distortion and chromatic aberrations. For example, plan-apochromatic objectives, having particularly sophisticated designs, provide optimum flat field correction combined with good achromatic properties.

Whatisthepurpose ofthe objectivelens inalightmicroscope

There are also often color-coded rings indicating different magnification values, e.g. black for 1 ×, yellow for 4 ×, green for 10 ×, etc.

Objectives for dark-field illumination are tentatively larger, providing extra space for the illumination light; therefore, they are typically used with larger threads.

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

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.

Microscope objectives are sometimes used for applications outside microscopy. For example, they can be used for tight focusing of laser beams, with spot sizes of a few micrometers or even below 1 μm. If the input beam is a collimated beam, an infinity-corrected objective will work best. The objective should have a numerical aperture which fits well to the beam divergence related to the required spot size. The input beam radius should also be chosen appropriately, i.e., calculated from the required spot size and the focal length. A difficulty may be to find out the focal length, as the objective barrel often only indicates the magnification, and the conversion to the focal length depends on the microscope design.

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.

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

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The higher the magnification, the higher is also the required numerical aperture because this is the factor which ultimately limits the achievable image resolution. There are different ways of calculating the image resolution and are slightly different circumstances, but they lead to similar resolution values, which are roughly <$\lambda / (2 NA)$>, where <$\lambda$> is the optical wavelength (about 400 to 700 nm) and NA is the numerical aperture. For example, an NA of 1 allows for an image resolution of roughly 250 nm for green light. For low magnification, an NA of 0.1 may be fully sufficient.

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

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)

What does thestagedo on a microscope

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)

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)

At least for high magnifications, the influence of a cover slip in terms of chromatic and spherical aberrations can be quite important. Therefore, objectives for use in fields like biology, where cover slips are often needed, are designed with integrated cover slip correction. The correction is often done for a standard slip thickness of 170 μm. A deviation of only 10 μm can already be quite problematic for an objective with a high NA of e.g. 0.95. Some objectives allow the adjustment of the corrected cover slip thickness.

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

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)

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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

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

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

Note that oil immersion may not work properly e.g. when observing a biological sample in an aqueous solution and the oil is only between the cover slip and the objective. One may have to use special water immersion objectives for such cases.

Older microscopes usually require finite-corrected objectives. Here, the object is supposed to be placed a little below the front focal plane of the objective, and the intermediate image occurs at a finite distance of e.g. 160 mm from the objective. Such an objective is designed for minimum image distortions in that configuration.

There are also reflective objectives, containing curved mirrors and no lenses. They are naturally achromatic and may be advantageous for operation in extreme wavelength domains. Also, they can exhibit lower losses of optical power.

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

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 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)

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

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.

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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.

The focal length of a microscope objective is typically between 2 mm and 40 mm. However, that parameter is often considered as less important, since magnification and numerical aperture are sufficient for quantifying the essential performance in a microscope.

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.

The microscope objective is a key component for reaching high performance of a microscope. It is the part which is placed next to the observed object, usually in a fairly small distance of a few millimeters. Usually, the microscope objective produces an intermediate image in the microscope, which is then further magnified with an eyepiece (ocular lens). Particularly in cases with high magnification, most of the magnification is provided by the objective.

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)

For such applications, chromatic aberrations are often no issue, so that one does not exploit the chromatic correction of the objective. Also, a wide field of view would not be required. On the other hand, a microscope objective for visible light may well not have ideal properties e.g. for launching near infrared light into a fiber, and its power handling capability is limited (but usually not specified). Therefore, a microscope objective may not be the ideal solution for such an application. However, it may have to be used, e.g. if no other lenses are available for reaching the required small spot size.

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 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)

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

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

What does theocular lensdo on a microscope

Note that a large magnification alone is not helpful if it only makes images larger without increasing the level of detail; see below the section on the numerical aperture.

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

Chromatic aberrations essentially result from the wavelength dependence of focal length. They lead to colored image distortions. For conventional microscopy, they can be quite relevant, in contrast to other types of optical microscopy, e.g. certain types of laser microscopy. Best suppression of chromatic aberrations is achieved with apochromatic objectives.

Another application is launching light into a single-mode fiber or collimating light from such a fiber. Again, the objective should have an appropriate numerical aperture of the order of that of the fiber. For more details, see the article on fiber launch systems.

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

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).

Another practically important factor is the working distance, i.e., the distance between the objective and the object. Small working distances are generally required for objectives with high NA, but also can to some extent be optimized as a design goal (possibly somewhat compromising the NA or the correction). For objectives with oil immersion, a relatively small working distance is actually good, since otherwise one would require more of the immersion fluid, and that would be more difficult to hold in place.

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

Note that it is essential not only to have a good transmittance over the full wavelength range, but also achromatic performance. In conventional light microscopes, this is needed to avoid colored image distortions. In confocal multi-photon fluorescence microscopes, it is important to have the same focus positions for infrared laser light as for the fluorescence light.

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)

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.

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

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

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.

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)

The objective lens is the most important part of a microscope and plays a central role in imaging an object onto the human eye or an image sensor for discerning the object’s detail. Microscope objectives are ideal for a range of science research, industrial, and general lab applications.

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

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 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

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

Whatisobjectivelens inmicroscope

In most cases, a microscope objective is mounted on the nosepiece of a microscope using a thread. Unfortunately, there are different thread sizes used by different manufacturers and for objectives of different kinds. In some cases, special adapters can be used for applying an objective to a microscope with different threads.

* 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.

Note that some microscope designs count on the correction of some residual aberrations of the objective by the ocular lens.

Types ofmicroscopeobjectives

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

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)

Microscopes often contain multiple objectives on a rotatable nosepiece, for example a scanning lens with only 4 × magnification, an intermediate one (the small objective lens) with 10 × and a high-resolution large objective with 40 × or 100 × magnification. The eye piece may contribute another factor 5 or 10 in magnification, for example.

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)

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.

MicroscopeObjectives magnification

Unfortunately, perfect solutions are not available; therefore, one has to accept certain trade-offs, which lead to different optimized solutions for different applications. For example, optimum flat field properties are most important for measurement microscopes; one may then tolerate somewhat larger chromatic aberrations.

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)

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.

Optical microscopes usually work based on imaging with visible light, i.e., in the wavelength region from 400 nm to 700 nm. Therefore, most microscope objectives are optimized for that wavelength range, with most emphasis on the region from 480 nm to 640 nm. However, there are objectives with an enhanced range of e.g. 400 nm to 950 nm, and others which work further in the infrared. For example, that is required for laser microscopes where infrared laser beams need to be transmitted.

* 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

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)

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 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)

Although a microscope objective is sometimes called the objective lens, it usually contains multiple lenses. The higher the numerical aperture and the higher the required image quality, the more sophisticated designs are needed. High-end microscope objectives may also involve aspheric lenses.

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

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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

The highest numerical apertures achievable with dry objectives, operated with air between the objective and the object, are approximately 0.95. Substantially higher values of e.g. 1.5 or even higher can be achieved with immersion objectives, where the gap between the object and the objective is filled with a liquid – water or some immersion oil with a higher refractive index, often somewhat above 1.5. Optimized immersion oils do not only have a high refractive index, but also a suitable viscosity and a low tendency for producing stains on the surfaces. They can be left on an objective over longer times without damaging it.

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).

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)

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

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.

The design of a high quality microscope objective is a rather sophisticated task, for which substantial optics expertise and powerful optics design software are required. Such designs involve complicated trade-offs, which should be properly handled according to the importance of different aspects for a particular application.

What does thestage clipsdo on a microscope

Most microscopes objectives are based on refractive optics, containing several lenses. For example, a simple low-NA objective may contain a meniscus lens and an achromat. A high-NA objective typically contains a more complicated combination of various types of lenses of hemispherical, meniscus, achromatic doublet and triplet type.

Edmund Optics offers a wide variety of microscopy components including microscope objectives, inverted and stereo microscopes, or optical filters that are ideal for use in microscopy setups. Microscope objectives are available in a range of magnifications and include infinity corrected, finite conjugate, and reflective objectives in industry leading brands such as Mitutoyo or Olympus. Microscope objectives are ideal for a range of research, industrial, life science, or general lab applications. Microscopy filters are ideal for isolating specific wavelengths in fluorescence imaging applications.

Modern microscopes mostly require infinity-corrected objectives, where the intermediate image of the objective alone lies at infinite distance. Here, one requires an additional tube lens in the microscope for generating the intermediate image at the diaphragm of the eyepiece.

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