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EKSMA Optics offers standard plano-convex, plano-concave, biconvex, biconcave, cylindrical lenses and lens kits made of BK7, UVFS or CaF2 optical materials. EKSMA Optics also has an extensive experience in manufacturing of custom optical lenses from a variety of other optical materials. Lenses of custom design can be produced in our CNC lens polishing facility and later coated for your application.

The curvature radii are taken as positive values for convex surfaces and negative for concave surfaces. Positive results are obtained for focusing lenses, negative results for defocusing lenses. The last term is relevant only for thick lenses with substantial curvature on both sides. The formula delivers the focal length within the paraxial approximation, not considering spherical aberrations, for example.

For some applications, in particular for focusing of imaging systems, it is essential than the focal length of an optical system can be fine adjusted. The following physical principles can be used:

The focal distance should also not be confused with the working distance, which is the distance between a specimen and the lens housing. Note that a specimen is not necessarily placed in the focal plane, e.g. when the input light to an objective is not collimated.

Considerable confusion arises from the fact that in the context of photo cameras the term effective focal length is also used with an entirely different meaning, as explained in the following.

where it is assumed that the beam radius at the focus is much smaller than the initial beam radius <$w_0$>. (This condition is violated for beams with a too small incident radius; the focus is then larger than according to the given equation.) Also, it is assumed that the beam radius is significantly larger than the wavelength <$\lambda$>, so that the paraxial approximation is valid.

Number of elements Depending on the design, a "lens" can have diferent internal lenses to correct the light and give a better image.

PPD manufactures custom, high precision optical components including spherical lenses, lens assemblies and spherical mirror substrates for imaging, machine vision and high energy laser applications from the ultraviolet (UV) through the near-infrared (NIR). Coated and uncoated optics are available from 2 mm to 8” in diameter and in a wide range of materials including fused silica, infrasil, N-BK7, YAG, SF11 and other high index glasses. If your radius of curvature is not yet determined, contact us for information on existing fabrication tooling and test plates, or send us your design specifications for a fully custom lens or mirror quotation.

FOVto focal length

What is “normal” is based on the size of the film/sensor. A full frame camera sports an image area that is about the same as the venerable 35mm film camera. This frame size measures 24mm height by 36mm length. A lens is considered to deliver a normal view if its focal length is about equal to the diagonal measurement of the frame. For the full frame this is about 45mm, however by tradition, we round this up to 50mm. For the smaller compact digital, the frame measures 16mm height by 24mm length. The normal focal length for this format is 30mm.

The price of a lens tends to increase as you go farther towards the extremes of focal length. Very wide and very long lenses tend to require a lot more glass and possibly a lot more corrections to get good image quality than a lens in the midrange. You also need to know that a lens is typically described by TWO numbers: the focal length and the maximum aperture (given as an f-number). Two lenses that have the same focal length(s) may have differing maximum apertures, or very different optical designs to achieve different goals (see: How do I choose a zoom lens for my Canon DSLR when I'm ready to move beyond the kit lens?)

The angle of view of the camera is determined by the ratio of the image size on the film and the focal length. Film-based cameras have for a long time mostly used 35-mm film (also called 135 film according to ISO Standard 1007), where the image size on the film is typically 36 mm × 24 mm. (The width of the film spool is 35 mm, somewhat larger than 24 mm, as the picture does not extend to the edges of the spool.) A standard objective then has a focal length of 50 mm. However, modern digital cameras (particularly the more compact ones) often contain image sensors which are smaller than 36 mm × 24 mm, so that an objective lens with a correspondingly smaller focal length (e.g. 32 mm instead of 50 mm) is required for obtaining the same field of view. As many photographers are still used to the previously valid relation between focal length and angle of view, it has become common to specify the effective focal length of an objective of a digital camera as that focal length which would give the same angle of view in combination with ordinary 35-mm film. For example, an objective with a true focal length of 32 mm may then be said to have an effective focal length of 50 mm and thus function as a standard objective, rather than e.g. a macro or tele objective.

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The equation shows that what determines the minimum possible beam radius is not the focal length <$f$> alone, but rather the ratio of <$f$> to the radius of the open aperture of the lens, which sets a maximum to the input beam radius <$w_0$>. For a focusing or collimation lens, that ratio is essentially the numerical aperture of the lens.

Short focal length lenses project tiny images and deliver a wide-angle view. Long focal length lenses project enlarged images; they are said to be telephoto. Lenses with variable focal lengths are called “zoom lenses”. The 50mm thru 300mm you mentioned is a zoom lens.

There's also the construction of the lens. The quality of the rings used to focus the lens, the quality of the motors for autofocus, etc. The body of the lens may be plastic or metal. Usually metal is better quality.

So, for example, a Canon EF 50mm f/1.2 lens is 3.4" in diameter whereas an EF 50mm f/1.8 is 2.7". The difference is more dramatic at longer focal lengths: an EF 200 f/2 is about 5" in diameter, whereas a EF 200 f/2.8 is about 3.3".

Equivalentfocal lengthcalculator

Laserton offers various types of lenses, including plano-convex, plano-concave, double convex, double concave, meniscus, ball, achromatic and cylindrical lenses.

While we call a lens "a lens," it's really a series of pieces of glass (lenses) in most cases (particularly a zoom lens). The more glass in it, usually the more expensive it is.

We offer precision optics lenses from 0.5 mm to 500 mm diameter. Surface quality can reach λ/10. All optical materials available.

Note that the locations of the left and right edges of the optical system (e.g. positions of outer lens surfaces, optical windows etc.) or its housing are not relevant for those definitions.

If a collimated Gaussian beam with beam radius <$w_0$> hits a focusing lens with focal length <$f$>, the beam radius of the beam waist (focus) after the lens can be calculated with the equation

I agree with the other answers. However, they've failed to answer the question of why some lenses of the same length or range cost different amounts. Some of it is due to the quality of the glass. Depending on how a piece of glass is made and what it's made of, it may pass none, some, or (almost) all of the light that hits it to the sensor/film. Better glass costs more.

There are several factors than define a lens size. A denser glass refracts light more than a low density one. This means that the low density needs more distance to focus than the denser one for example.

Lensequation

If a divergent (rather than collimated) beam hits a focusing lens, the distance <$b$> from the lens to the focus becomes larger than <$f$> (Figure 2). The lens equation states that

Unfortunately, the terms are also used differently by other authors. For example, it happens that a focal distance is assumed to be the same as a focal length. Therefore, some product catalogs specify focal lengths, which should actually be called focal distances, and in addition the effective focal length.

When there are two numbers that means the lens is a zoom lens, where you can vary the focal length over a range. The first number is the wide end of the range, while the second number is the telephoto end of the range.

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Edmund Optics offers the world’s largest inventory of off-the-shelf optical components, which includes an extensive selection of stock optical lenses such as achromatic lenses or aspheric lenses. Many of Edmund Optics’ lenses are offered with a variety of coating options for the ultraviolet (UV), visible, or infrared (IR) spectrum.

Artifex Engineering offers customised optical lenses such as achromatic or cylindrical lenses for almost any application in the UV to IR spectrum. Special requirements such as segmenting and black painted edges can be made on request. Visit our product page for more information. We look forward to your inquiry.

Lenscalculator

A common (but not universally used) approach for the definition of focal lengths of extended systems is based on geometrical optics. For finding the front focal point, one calculates rays which are horizontal on the back side (see Figure 2), using the paraxial approximation. The optical system is considered as a “black box”, where one does not care about the actual ray paths; instead, one works with internal rays which are extrapolated from the outer rays. Based on those extrapolated rays, one can define the front principal plane (or first principal plane). The front focal length is then the distance between the front focal point (in the front focal plane) and the front principal plane (see Figure 2). Some authors define the focal length to be negative in the situation of Figure 2 because the focal point is located before the front principal plane; others take the absolute value.

Do not confuse this 35mm with the previous one. On this case the most widley used camera were the 35mm film (phisical dimension of the wide part of the film) As this were the most popular, when the sensor is of a diferent dimension is common to define the angle of view as an equivalent to the 35mm film.

The following equation allows one to calculate the dioptric power and thus the focal length of lens made of a material with refractive index <$n$> and with curvature radii <$R_1$> and <$R_2$> on the two surfaces:

Enter input values with units, where appropriate. After you have modified some values, click a “calc” button to recalculate the field left of it.

OPTOMAN's AR-coated lenses are optimized for high laser power applications. These lenses can be used for intracavity, multi-kW CW, and ultrafast pulse applications. Sputtered anti-reflective coatings feature reflectance per surface down to R < 0.01%.

For an optical system, which may consist of multiple lenses and other optical elements, the above definition of the focal length cannot be used, as it is not clear a priori for an extended system where to measure the distance to the focus: from the entrance into the optical system, from the exit, the middle, or some other position? In principle, an arbitrary definition of a reference point (e.g. the entrance or the middle) could be used, but that would in general mean that some common rules can not be applied, which e.g. hold for the radius of the beam waist at a focus behind some lens with a given focal length (see below), or the possible magnification of a telescope containing that optical system.

Avantier is proficient in producing customized lenses for all kinds of applications, ranging from prototyping to large-scale production.

Curved laser mirrors usually have a curvature radius somewhere between 10 mm and 5 m. The fabrication of dielectric mirror coatings can be more difficult for very strongly curved mirror substrates, but with refined techniques it is possible to reach focal lengths of only a few millimeters, as required for some miniature lasers.

A lens with a given focal length <$f$> (taken as positive in the case of a focusing lens) creates a radially varying phase delay for a laser beam according to the following equation:

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The bottom line is that different photographers have different needs: some have to work within a budget or want a lens that's easy to carry; others are happy to pay the price for a lens that's built better and/or is more capable.

Enter input values with units, where appropriate. After you have modified some values, click a “calc” button to recalculate the field left of it.

Our spherical lenses are widely used in a variety of industrial and detection cameras, microscopic objectives, spectral imaging, machine vision, infrared night vision and sensing, thermal imaging, environmental protection and biology. Lenses can be equipped with anti-reflective coatings, HR coatings and metallic mirror coatings, dielectric films and spectroscopic films.

Focal length of aconvexlens

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Whether this rule can also be applied to an extended optical system with focal length <$f$> depends on the applied definition of <$f$>. It is useful to specify an effective focal length which is valid for such relations.

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When a lens has two numbers, we say it has a focal-range, which means it can take on any focal-length within the range. So, if the lens is a 50-200mm, then you can set it at any focal-length between 50 and 200. Not just whole numbers be really anything, could be 107.5mm if you like. Of course, only some focal-lengths are labelled, so you cannot be sure if you set it to 56 or 57mm.

Ordinary lenses, working on the basis of refraction, have a focal length which is slightly wavelength-dependent due to the wavelength dependence of the refractive index (–> chromatic dispersion). This effect leads to chromatic aberrations of imaging systems and similar problems in other applications where an optical system is used for a wide range of optical wavelengths. Lens combinations (e.g., objectives for photographic cameras) can be designed such that chromatic aberrations are minimized. Most common is the use of achromatic doublets, i.e., lenses consisting of two different glass materials chosen such that the overall chromatic aberrations are largely canceled.

One big difference is the maximum aperture. The f-number of a lens is determined by the focal length divided by the diameter of the "entrance pupil," i.e. the aperture as it appears from the front of the lens. To create a wider entrance pupil, you need a wider aperture and a larger lens.

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When a lens has a range (for example 70-300 mm) this means that has internal elements than can move back and foward and modify this focal length, therefore the field of view.

The focal length of the lens is the number given in millimeters. It basically describes the field of view of the lens and its magnification. Most folks think of shorter lenses as wide angle and longer lenses as telephoto, and certain subjects tend to lend themselves to one type of lens vs. another. (See: the Nikon lens simulator).

Between this theorical lenses: 55mm-200mm or a 55mm-600mm The biggest number means a more powerfull telephoto. So a far object will look bigger.

For a defocusing system, the front focal plane can be located on the output side; it contains a virtual focal point. Again, the focal length is the distance between principal plane and focal plane.

Focal length ofmirror formula

Similarly, one can define the back focal plane (or second focal plane) and back principal plane (or second principal plane), where horizontal rays occur on the left side, while on the right side one has converging rays for a focusing system and diverging rays for a defocusing system. If the refractive index is the same on the input and output side (e.g. ≈1 for air), the front focal length and back focal length are identical (apart from possible sign differences used by some authors) and can thus simply called the focal length. The two principal planes, however, generally do not coincide for thick lenses, and they can even lie outside a lens.

For a focusing lens, this means a reduced phase delay for increasing <$r$> coordinate. Note that there are different sign conventions in wave optics, where a phase delay can correspond to a positive or negative change of a phasor (complex amplitude).

Many variables affect the cost of a lens. These include things like image quality, build quality (e.g. weather sealing, barrel material, etc.), image stabilization, special materials like fluorite or special coatings, market size, etc. Most of us would probably prefer to carry the EF 200 f/2.8, which at $749 and 1.7 lbs is a lot more affordable and portable than the $5699, 5.6 lb EF 200 f/2. On the other hand, there are also photographers out there for whom the benefits of the f/2 lens outweigh the much larger cost, size, and weight.

Inclusive some large telephoto lenses can be Reflective rather than Refractive, so they use internal mirrors to bounce the light inside and shorten the overall length of the lens.

One more question. What does the first set of mm numbers represent and what does the second (higher) number represent? Which lens is going to magnify something far away better? A 55mm-200mm or a 55mm-600mm? Simple beginner language works best.

The Model 02-014-1 is an air spaced, computer designed multi-element lens that is diffraction-limited when used with fibers having core diameters as large as 1200 microns. Operational wavelength is 1064 nm. The 02-014 reimages the emitting surface of the fiber with a 0.67× demagnification. Focused spot sizes are significantly smaller than those achievable with single-element lenses used in a similar collimating/focusing configuration. All optical elements are fabricated from high laser-damage resistant glasses and are anti-reflection coated to reduce reflectance per surface to 0.13%. The working distance between the lens and the target is sufficiently large to allow use of a gas nozzle to enhance the cutting or welding process and to prevent debris from depositing on the lens surface.

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The formula ignores the constant part of the optical phase change as well as optical aberrations. Note that depending on the function of the lens – for example, focusing collimated input beams or refocusing divergent light –, higher-order terms in the phase profile may be required to avoid optical aberrations.

How far a lens sees is the wrong way to think about it. With very specialized exceptions, all lenses can focus until infinity. The right metric for how close you can magnify something is called magnification. Read this answer to a relevant question to understand how these relate.

The numbers measured in millimeters (mm) represent focal length. If there are two, they're the shortest and longest focal length of a zoom lens. The larger the number, the narrower the angle of view. On a full-frame DSLR, a 200mm lens will fill the frame with a view that's about 10° wide; a 600mm lens captures a view that's only around 3.4° wide. So, the 600mm lens makes a subject at the same distance seem larger than the 200mm lens does, and they're of course both the same at the 55mm end of the zoom range. On the other hand, a 55-600mm zoom lens would typically be a lot larger and heavier than a 55-200mm zoom.

Hyperfocal distance calculator

In this case for example a 80mm lens could be equivalent in terms of the field of view on a big sensor or 15mm on a small sensor (F) remains the same.

As to what span or range of the zoom is best: Lenses are tools and some are better than others. Lenses with a large zoom span are difficult to make; thus good ones are very expensive. Suffice to say, you get what you pay for.

The explained definition delivers a focal length which can also be used in equations for the size of the focus (see below), for example.

The camera lens acts like a projector lens. Its job is to project an image of the outside world on the surface of film or digital image sensor. The camera lens is a converging lens. Light from a far distant object enters the lens as parallel rays. The lens bends these rays inward so they trace out the shape of a cone. When we focus, we are adjusting lens to film/sensor distance so the apex of the cone just kisses the surface of film/sensor. We measure this distance, lens to film/sensor when the subject is at infinity (∞ as far as the eye can see). It is costmary to measure using the metric system, thus the millimeter is used. We label this distance the focal length. A 50mm lens means the lens to image distance is 50mm (about 2 inches) when the camera is imaging a distant subject.

Focal length

For completness, you will sometimes encounter another measurement in mm on the lens which is the width of the filter-thread. This only dictates the diameter needed for a filter to mount directly on the lens instead of requiring an adapter-ring. Most lens have one but some lens do not, mostly on extreme wide ones such as fisheyes where any filter would obscure the angle-of-view partly.

What does the first set of mm numbers represent and what does the second (higher) number represent? Which lens is going to magnify something far away better? A 55mm-200mm or a 55mm-600mm? Simple beginner language works best.

Taking your examples, the lens with a 600mm maximum focal-length has the smallest angle-of-view and therefore will magnify a distant object more. This type of lens is mostly used for bird and wildlife photography.

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Note that the lens equation applies for rays, assuming that the paraxial approximation is valid, i.e., all angles relative to the beam axis remain small.

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The dioptric power (also called focusing power) of a lens is defined as the inverse of the effective focal length (which is the same is the front and back focal length if the median on both sides of the optics is the same). This means that a strongly focusing lens has a small focal length, but a large dioptric power. For prescription glasses, it is common the specify the dioptric power, whereas the focal length is specified for standard lenses, microscope objectives, and photographic objectives.

Various types of optical systems (e.g. microscope objectives and curved laser mirrors) can focus or defocus light, and the focal length is used for quantifying such effects. The simplest case is that of a thin focusing lens (Figure 1a). If a sufficiently large collimated beam of light is incident on the lens, the beam will be focused, and the focal length is the distance from the lens to that focus (assuming that the lens is surrounded by vacuum or air, not by some dense substance with a significant refractive index). For a defocusing lens (Figure 1b), the focal length is the distance from the lens to the virtual focus (indicated by the dashed lines), taken as a negative value. Some authors use different sign conventions, however, in particularly concerning the front and back focal length (see below).

In a pinhole camera the distance is exactly that, a phisical distance. On a glass lens this distance could not be exactly that becouse lens design, components etc. That is why I mention theorical.

Curved mirrors are often used for focusing or defocusing light. For example, within laser resonators curved laser mirrors with dielectric coatings are more commonly used than lenses, mainly because they introduce lower losses.

The measurement you refer to is most likely focal-length. A shorter focal-length gives a wide angle of view. Conversely a longer one gives a smaller angle-of-view. When a lens has a single number, the angle of view is mostly fixed. This is what we call a prime lens.

I'm confused about lenses and numbers. Why are some lenses ex. 50mm-300mm Different sizes? Some lenses with the same mm numbers are huge and some are small... What's the difference? Also the prices differ. Some lenses are cheap and the same number mm lens is outrageous and the same size.

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A mirror with a curvature radius <$R$> of the surface has a focal length <$f = R / 2$>, if the beam axis is normal to the mirror surface. (We take positive signs for concave curvatures and focusing mirrors.) If there is some non-zero angle <$\theta$> between the beam axis and the normal direction, the focal length is <$f_{\tan} = (R / 2) \cdot \cos \theta$> in the tangential direction (i.e., within the plane of incidence) and <$f_{sag} = (R / 2) / \cos \theta$> in the sagittal direction.

In contrast to focal lengths, focal distances are related not to the principal planes but rather to the vertex points of lenses (not caring about a housing, which may be further extended). The front focal distance is thus the distance between front focal point and the entrance surface of the optics, while the back focal distance is the distance between the back surface and the back focal point.

One may eliminate chromatic aberrations altogether by using optical systems with mirrors only. A curved mirror with radius of curvature <$R$> has a focal length <$f = R / 2$> (for normal incidence), determined only by the geometry and thus independent of the wavelength. On the other hand, for non-normal incidence the focal length in the tangential direction is decreased by the cosine of the angle of incidence, and increased by the inverse cosine of that angle in the sagittal direction. Therefore, such mirrors can introduce astigmatism.

Imagine a pinhole camera obscura. The distance from this pinhole to the back wall is the focal distance (A), which eventually defines the viewing angle (F).

where <$a$> is the distance from the original focus to the lens. This shows that <$b \approx f$> if <$a \gg f$>, but <$b > f$> otherwise. That relation can be intuitively understood: a focusing power <$1 / a$> would be required to collimate the incident beam (i.e. to remove its beam divergence), so that only a focusing power <$1 / f - 1 / a$> is left for focusing.

Low-loss ion-beam-sputtered anti-reflection (AR) coatings with reflectivity less than 0.1% per surface and low-absorption high reflector mirror coatings are available on PPD lenses or can be applied to customer supplied substrates. PPD uses only IBS thin film deposition technology because it is a repeatable process which results in coatings that are durable, stable and easy to clean.

Different sign conventions for focal lengths are used in the literature. For example, one may have a negative front focal length if the front focal point lies before the front principal plane. Obviously, any equations involving focal lengths should be used with the assumed sign conventions.