The typical appearance of a bright-field microscopy image is a dark sample on a bright background, hence the name. An example bright-field micrograph. This ...

Strategy Once a value for the diffraction grating’s slit spacing d has been determined, the angles for the sharp lines can be found using the equation

The following table provides an overview of what focal lengths are required to be considered a wide angle or telephoto lens, in addition to their typical uses. Please note that focal lengths listed are just rough ranges, and actual uses may vary considerably; many use telephoto lenses in distant landscapes to compress perspective, for example.

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This is primarily because slight rotational vibrations are magnified greatly with distance, whereas if only up and down or side to side vibrations were present, the laser's bright spot would not change with distance.

Any of the above problems is present to some degree with any lens. In the rest of this tutorial, when a lens is referred to as having lower optical quality than another lens, this is manifested as some combination of the above artifacts. Some of these lens artifacts may not be as objectionable as others, depending on the subject matter.

An electric current through hydrogen gas produces several distinct wavelengths of visible light. What are the wavelengths of the hydrogen spectrum, if they form first-order maxima at angles and when projected on a diffraction grating having 10,000 lines per centimeter?

An f-number of X may also be displayed as 1:X (instead of f/X), as shown below for the Canon 70-200 f/2.8 lens (whose box is also shown above and lists f/2.8).

Find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a difraction grating having 1500 lines per centimeter.

Check Your Understanding If the line spacing of a diffraction grating d is not precisely known, we can use a light source with a well-determined wavelength to measure it. Suppose the first-order constructive fringe of the emission line of hydrogen is measured at using a spectrometer with a diffraction grating. What is the line spacing of this grating?

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The analysis shown below also applies to diffraction gratings with lines separated by a distance d. What is the distance between fringes produced by a diffraction grating having 125 lines per centimeter for 600-nm light, if the screen is 1.50 m away? (Hint: The distance between adjacent fringes is assuming the slit separation d is comparable to )

Note that larger aperture openings are defined to have lower f-numbers (often very confusing). These two terms are often mistakenly interchanged; the rest of this tutorial refers to lenses in terms of their aperture size. Lenses with larger apertures are also described as being "faster," because for a given ISO speed, the shutter speed can be made faster for the same exposure. Additionally, a smaller aperture means that objects can be in focus over a wider range of distance, a concept also termed the depth of field.

Notice that in both equations, we reported the results of these intermediate calculations to four significant figures to use with the calculation in part (b).

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Finally, some zoom lenses on digital SLR and compact digital cameras often list a range of maximum aperture, because this may depend on how far one has zoomed in or out. These aperture ranges therefore refer only to the range of maximum aperture, not overall range. A range of f/2.0-3.0 would mean that the maximum available aperture gradually changes from f/2.0 (fully zoomed out) to f/3.0 (at full zoom). The primary benefit of having a zoom lens with a constant maximum aperture is that exposure settings are more predictable, regardless of focal length.

Minimum apertures for lenses are generally nowhere near as important as maximum apertures. This is primarily because the minimum apertures are rarely used due to photo blurring from lens diffraction, and because these may require prohibitively long exposure times. For cases where extreme depth of field is desired, then smaller minimum aperture (larger maximum f-number) lenses allow for a wider depth of field.

Analyzing the interference of light passing through two slits lays out the theoretical framework of interference and gives us a historical insight into Thomas Young’s experiments. However, most modern-day applications of slit interference use not just two slits but many, approaching infinity for practical purposes. The key optical element is called a diffraction grating, an important tool in optical analysis.

(a) Show that a 30,000 line per centimeter grating will not produce a maximum for visible light. (b) What is the longest wavelength for which it does produce a first-order maximum? (c) What is the greatest number of line per centimeter a diffraction grating can have and produce a complete second-order spectrum for visible light?

Take the same simulation we used for double-slit diffraction and try increasing the number of slits from to . The primary peaks become sharper, and the secondary peaks become less and less pronounced. By the time you reach the maximum number of , the system is behaving much like a diffraction grating.

The aperture range of a lens refers to the amount that the lens can open up or close down to let in more or less light, respectively. Apertures are listed in terms of f-numbers, which quantitatively describe relative light-gathering area (depicted below).

In reality, the number of slits is not infinite, but it can be very large—large enough to produce the equivalent effect. A prime example is an optical element called a diffraction grating. A diffraction grating can be manufactured by carving glass with a sharp tool in a large number of precisely positioned parallel lines, with untouched regions acting like slits ((Figure)). This type of grating can be photographically mass produced rather cheaply. Because there can be over 1000 lines per millimeter across the grating, when a section as small as a few millimeters is illuminated by an incoming ray, the number of illuminated slits is effectively infinite, providing for very sharp principal maxima.

(a) Find the maximum number of lines per centimeter a diffraction grating can have and produce a maximum for the smallest wavelength of visible light. (b) Would such a grating be useful for ultraviolet spectra? (c) For infrared spectra?

Focal lengthcamera

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Note: Calculator assumes that camera is oriented such that the maximum subject dimension given by "subject size" is in the camera's longest dimension. Calculator not intended for use in extreme macro photography.

Note: For a more quantitative and technical discussion of the above topic, please see thetutorial on camera lens quality: MTF, resolution & contrast.

Where are diffraction gratings used in applications? Diffraction gratings are commonly used for spectroscopic dispersion and analysis of light. What makes them particularly useful is the fact that they form a sharper pattern than double slits do. That is, their bright fringes are narrower and brighter while their dark regions are darker. Diffraction gratings are key components of monochromators used, for example, in optical imaging of particular wavelengths from biological or medical samples. A diffraction grating can be chosen to specifically analyze a wavelength emitted by molecules in diseased cells in a biopsy sample or to help excite strategic molecules in the sample with a selected wavelength of light. Another vital use is in optical fiber technologies where fibers are designed to provide optimum performance at specific wavelengths. A range of diffraction gratings are available for selecting wavelengths for such use.

The primary advantages of prime lenses are in cost, weight and speed. An inexpensive prime lens can generally provide as good (or better) image quality as a high-end zoom lens. Additionally, if only a small fraction of the focal length range is necessary for a zoom lens, then a prime lens with a similar focal length will be significantly smaller and lighter. Finally, the best prime lenses almost always offer better light-gathering ability (larger maximum aperture) than the fastest zoom lenses — often critical for low-light sports/theater photography, and when a shallow depth of field is necessary.

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All but the simplest cameras contain lenses which are actually comprised of several "lens elements." Each of these elements directs the path of light rays to recreate the image as accurately as possible on the digital sensor. The goal is to minimize aberrations, while still utilizing the fewest and least expensive elements.

An opal such as that shown in (Figure) acts like a reflection grating with rows separated by about If the opal is illuminated normally, (a) at what angle will red light be seen and (b) at what angle will blue light be seen?

Calculating Typical Diffraction Grating Effects Diffraction gratings with 10,000 lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.00 m away. (a) Find the angles for the first-order diffraction of the shortest and longest wavelengths of visible light (380 and 760 nm, respectively). (b) What is the distance between the ends of the rainbow of visible light produced on the screen for first-order interference? (See (Figure).)

The focal length of a lens may also have a significant impact on how easy it is to achieve a sharp handheld photograph. Longer focal lengths require shorter exposure times to minimize blurring caused by shaky hands. Think of this as if one were trying to hold a laser pointer steady; when shining this pointer at a nearby object its bright spot ordinarily jumps around less than for objects farther away.

For compact digital cameras, lenses listed with a 3X, 4X, etc. zoom designation refer to the ratio between the longest and shortest focal lengths. Therefore, a larger zoom designation does not necessarily mean that the image can be magnified any more (since that zoom may just have a wider angle of view when fully zoomed out). Additionally, digital zoom is not the same as optical zoom, as the former only enlarges the image through interpolation. Read the fine-print to ensure you are not misled.

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470-nm blue light at an angle of ?

a. , , , ; b. , , , ; c. Decreasing the number of lines per centimeter by a factor of x means that the angle for the x-order maximum is the same as the original angle for the first-order maximum.

Many will say that focal length also determines the perspective of an image, but strictly speaking, perspective only changes with one's location relative to their subject. If one tries to fill the frame with the same subjects using both a wide angle and telephoto lens, then perspective does indeed change, because one is forced to move closer or farther from their subject. For these scenarios only, the wide angle lens exaggerates or stretches perspective, whereas the telephoto lens compresses or flattens perspective.

Other considerations include cost, size and weight. Lenses with larger maximum apertures are typically much heavier, larger and more expensive. Size/weight may be critical for wildlife, hiking and travel photography because all of these often utilize heavier lenses, or require carrying equipment for extended periods of time.

Note: The location where light rays cross is not necessarily equal to the focal length,as shown above, but is instead roughly proportional to this distance.

Other factors may also be influenced by lens focal length. Telephoto lenses are more susceptible to camera shake since small hand movements become magnified, similar to the shakiness experience while trying to look through binoculars. Wide angle lenses are generally more resistant to flare, in part because the designers assume that the sun is more likely to be within the frame. A final consideration is that medium and telephoto lenses generally yield better optical quality for similar price ranges.

Focal lengthformula

A common rule of thumb for estimating how fast the exposure needs to be for a given focal length is the one over focal length rule. This states that for a 35 mm camera, the exposure time needs to be at least as fast as one over the focal length in seconds. In other words, when using a 200 mm focal length on a 35 mm camera, the exposure time needs to be at least 1/200 seconds — otherwise blurring may be hard to avoid. See the tutorial on reducing camera shake with hand-held photos for more on this topic.

Optical aberrations occur when points in the image do not translate back onto single points after passing through the lens — causing image blurring, reduced contrast or misalignment of colors (chromatic aberration). Lenses may also suffer from uneven, radially decreasing image brightness (vignetting) or distortion. Move your mouse over each of the options below to see how these can impact image quality in extreme cases:

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Focus distance

FOV tofocal length

The focal length of a lens determines its angle of view, and thus also how much the subject will be magnified for a given photographic position. Wide angle lenses have short focal lengths, while telephoto lenses have longer corresponding focal lengths.

Significance The large distance between the red and violet ends of the rainbow produced from the white light indicates the potential this diffraction grating has as a spectroscopic tool. The more it can spread out the wavelengths (greater dispersion), the more detail can be seen in a spectrum. This depends on the quality of the diffraction grating—it must be very precisely made in addition to having closely spaced lines.

Diffraction Gratings Copyright © by Samuel J. Ling; Jeff Sanny; and William Moebs is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

Portrait and indoor sports/theater photography often requires lenses with very large maximum apertures, in order to be capable of a narrower depth of field or a faster shutter speed, respectively. The narrow depth of field in a portrait helps isolate the subject from their background. For digital SLR cameras, lenses with larger maximum apertures provide significantly brighter viewfinder images — possibly critical for night and low-light photography. These also often give faster and more accurate auto-focusing in low-light. Manual focusing is also easier because the image in the viewfinder has a narrower depth of field (thus making it more visible when objects come into or out of focus).

Keep in mind that using a zoom lens does not necessarily mean that one no longer has to change their position; zooms just increase flexibility. In the example below, the original position is shown along with two alternatives using a zoom lens. If a prime lens were used, then a change of composition would not have been possible without cropping the image (if a tighter composition were desirable). Similar to the example in the previous section, the change of perspective was achieved by zooming out and getting closer to the subject. Alternatively, to achieve the opposite perspective effect, one could have zoomed in and moved farther from the subject.

Calculate the wavelength of light that has its second-order maximum at when falling on a diffraction grating that has 5000 lines per centimeter.

Since there are 10,000 lines per centimeter, each line is separated by 1/10,000 of a centimeter. Once we know the angles, we an find the distances along the screen by using simple trigonometry.

A zoom lens is one where the photographer can vary the focal length within a pre-defined range, whereas this cannot be changed with a "prime" or fixed focal length lens. The primary advantage of a zoom lens is that it is easier to achieve a variety of compositions or perspectives (since lens changes are not necessary). This advantage is often critical for dynamic subject matter, such as in photojournalism and children's photography.

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Camera Type Digital SLR with CF of 1.6X Digital SLR with CF of 1.5X Digital SLR with CF of 1.3X Digital compact with 1/3" sensor Digital compact with 1/2.5" sensor Digital compact with 1/2.3" sensor Digital compact with 1/1.8" sensor Digital compact with 1/1.7" sensor Digital compact with 2/3" sensor Digital compact with a 1" sensor Digital SLR with 4/3" sensor 35 mm (full frame) APS-C 6x4.5 cm 6x6 cm 6x7 cm 5x4 inch 10x8 inch

The analysis of multi-slit interference in Interference allows us to consider what happens when the number of slits N approaches infinity. Recall that secondary maxima appear between the principal maxima. We can see there will be an infinite number of secondary maxima that appear, and an infinite number of dark fringes between them. This makes the spacing between the fringes, and therefore the width of the maxima, infinitesimally small. Furthermore, because the intensity of the secondary maxima is proportional to , it approaches zero so that the secondary maxima are no longer seen. What remains are only the principal maxima, now very bright and very narrow ((Figure)).

Focal length

Understanding camera lenses can help add more creative control to digital photography. Choosing the right lens for the task can become a complex trade-off between cost, size, weight, lens speed and image quality. This tutorial aims to improve understanding by providing an introductory overview of concepts relating to image quality, focal length, perspective, prime vs. zoom lenses and aperture or f-number.

*Note: Lens focal lengths are for 35 mm equivalent cameras. If you have a compact or digital SLR camera, then you likely have a different sensor size. To adjust the above numbers for your camera, please use the focal length converter in the tutorial on digital camera sensor sizes.

A diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum be for 520-nm-wavelength green light?

(a) What do the four angles in the preceding problem become if a 5000-line per centimeter diffraction grating is used? (b) Using this grating, what would the angles be for the second-order maxima? (c) Discuss the relationship between integral reductions in lines per centimeter and the new angles of various order maxima.

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What is the spacing between structures in a feather that acts as a reflection grating, giving that they produce a first-order maximum for 525-nm light at a angle?

Focaldistance vsfocal length

Keep in mind that this rule is just for rough guidance; some may be able to hand hold a shot for much longer or shorter times. For users of digital cameras with cropped sensors, one needs to convert into a 35 mm equivalent focal length.

When one is considering purchasing a lens, specifications ordinarily list the maximum (and maybe minimum) available apertures. Lenses with a greater range of aperture settings provide greater artistic flexibility, in terms of both exposure options and depth of field. The maximum aperture is perhaps the most important lens aperture specification, which is often listed on the box along with focal length(s).

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Why would one intentionally restrict their options by using a prime lens?Prime lenses existed long before zoom lenses were available, and still offer many advantages over their more modern counterparts. When zoom lenses first arrived on the market, one often had to be willing to sacrifice a significant amount of optical quality. However, more recent high-end zoom lenses generally do not produce noticeably lower image quality, unless scrutinized by the trained eye (or in a very large print).

What is the distance between lines on a diffraction grating that produces a second-order maximum for 760-nm red light at an angle of ?

Illustration showing how to measure the focal length of a converging lens using a distant object. Diverging (or Concave) lenses.

Diffraction gratings work both for transmission of light, as in (Figure), and for reflection of light, as on butterfly wings and the Australian opal in (Figure). Natural diffraction gratings also occur in the feathers of certain birds such as the hummingbird. Tiny, finger-like structures in regular patterns act as reflection gratings, producing constructive interference that gives the feathers colors not solely due to their pigmentation. This is called iridescence.

Also note that just because the maximum aperture of a lens may not be used, this does not necessarily mean that this lens is not necessary. Lenses typically have fewer aberrations when they perform the exposure stopped down one or two f-stops from their maximum aperture (such as using a setting of f/4.0 on a lens with a maximum aperture of f/2.0). This *may* therefore mean that if one wanted the best quality f/2.8 photograph, a f/2.0 or f/1.4 lens may yield higher quality than a lens with a maximum aperture of f/2.8.

Perspective control can be a powerful compositional tool in photography, and often determines one's choice in focal length (when one can photograph from any position). Move your mouse over the above image to view an exaggerated perspective due to a wider angle lens. Note how the subjects within the frame remain nearly identical — therefore requiring a closer position for the wider angle lens. The relative sizes of objects change such that the distant doorway becomes smaller relative to the nearby lamps.