Applications of Diffraction, Interference, and Coherence, Diffraction and Interference | Physics

Learning objectives

Section Key Terms

differential interference contrast (DIC)	diffraction grating	iridescence	laser
monochromator	Rayleigh criterion	resolution

Wave-Based Applications of Light

In 1917, Albert Einstein was thinking about photons and excited atoms. He considered an atom excited by a certain amount of energy and what would happen if that atom were hit by a photon with the same amount of energy. He suggested that the atom would emit a photon with that amount of energy, and it would be accompanied by the original photon. The exciting part is that you would have two photons with the same energy and they would be in phase. Those photons could go on to hit other excited atoms, and soon you would have a stream of in-phase photons. Such a light stream is said to be coherent. Some four decades later, Einstein’s idea found application in a process called, light amplification by stimulated emission of radiation. Take the first letters of all the words (except by and “of”) and write them in order. You get the word laser (see Figure_17_01_RayWave (a)), which is the name of the device that produces such a beam of light.

Laser beams are directional, very intense, and narrow (only about 0.5 mm in diameter). These properties lead to a number of applications in industry and medicine. The following are just a few examples:

This chapter began with a picture of a compact disc (see Figure_17_00_CDcolors). Those audio and data-storage devices began replacing cassette tapes during the 1990s. CDs are read by interpreting variations in reflections of a laser beam from the surface.
Some barcode scanners use a laser beam.
Lasers are used in industry to cut steel and other metals.
Lasers are bounced off reflectors that astronauts left on the Moon. The time it takes for the light to make the round trip can be used to make precise calculations of the Earth-Moon distance.
Laser beams are used to produce holograms. The name hologram means entire picture (from the Greek holo-, as in holistic), because the image is three-dimensional. A viewer can move around the image and see it from different perspectives. Holograms take advantage of the wave properties of light, as opposed to traditional photography which is based on geometric optics. A holographic image is produced by constructive and destructive interference of a split laser beam.
One of the advantages of using a laser as a surgical tool is that it is accompanied by very little bleeding.
Laser eye surgery has improved the vision of many people, without the need for corrective lenses. A laser beam is used to change the shape of the lens of the eye, thus changing its focal length.

An interesting thing happens if you pass light through a large number of evenly-spaced parallel slits. Such an arrangement of slits is called a diffraction grating. An interference pattern is created that is very similar to the one formed by double-slit diffraction (see Figure_17_01_2slit2 and Figure_17_01_2slit3). A diffraction grating can be manufactured by scratching glass with a sharp tool to form a number of precisely positioned parallel lines, which act like slits. Diffraction gratings work both for transmission of light, as in Figure_17_02_Grating, and for reflection of light, as on the butterfly wings or the Australian opal shown in Figure_17_02_Grating2, or the CD pictured in the opening illustration of this chapter. In addition to their use as novelty items, 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 do double slits. That is, their bright regions are narrower and brighter, while their dark regions are darker. Figure_17_02_Grating3 shows idealized graphs demonstrating the sharper pattern. Natural diffraction gratings occur in the feathers of certain birds. Tiny, fingerlike structures in regular patterns act as reflection gratings, producing constructive interference that gives the feathers colors not solely due to their pigmentation. The effect is called iridescence.

View original figure (external; image not reproduced in this text edition)

Original figure description: (a) Drawing of a vertical screen with five equally spaced horizontal slits that take up the middle third. A single blue arrow to the left of the barrier point to the right. Five blue arrows from the five slits point to the right, to five small diagrams arranged vertically. (b) Five small diagrams arranged vertically. The middle diagram is a white rectangle. It is labeled “Central white.” Above it is a square with colored bands; from the top, they are red, yellow, green, blue, and purple. The square is labeled “First-order rainbow.” Above the first rainbow is another small square, with the same colors as the one below, but fainter. It is labeled “Second-order rainbow.” Below the central white square is another square with colored bands. They are purple, blue, green, yellow, and red (the opposite order from the upper rainbows), and the square is labeled “First-order rainbow.” The lowest of the five diagrams is a fainter version of the square above it. It is labeled “Second-order rainbow.”

A diffraction grating consists of a large number of evenly-spaced parallel slits. (a) Light passing through the grating is diffracted in a pattern similar to a double slit, with bright regions at various angles. (b) The pattern obtained for white light incident on a grating. The central maximum is white, and the higher-order maxima disperse white light into a rainbow of colors.

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Original figure description: (a) Photograph of an opal, with a rounded triangular shape. Most of the upper portion of the triangle is red and yellow. The lower portion is blue, green, and purple. (b) Photograph of a butterfly on a leaf. The wings are blue with white spots at the points of the wings and black bands at the rear edges of the wings.

(a) This Australian opal and (b) the butterfly wings have rows of reflectors that act like reflection gratings, reflecting different colors at different angles. (credit: (a) Opals-On-Black.com, via Flickr (b) whologwhy, Flickr)

View original figure (external; image not reproduced in this text edition)

Original figure description: (a) Graph labeled “double slit.” A sine curve with three peaks is plotted with its troughs on a horizontal axis. Three points on the axis are labeled, corresponding to three maxima. Left to right, the points are labeled “m equals 1,” m equals zero,” and “m equals 1.” (b) Graph labeled “grating.” A curve with three tall narrow peaks is plotted with its troughs on a horizontal axis. On either side of the three peaks are two much smaller peaks (the larger peaks are separated by a total of four smaller peaks). Three points on the axis are labeled, corresponding to three maxima. Left to right, the points are labeled “m equals 1,” m equals zero,” and “m equals 1.”

Idealized graphs of the intensity of light passing through a double slit (a) and a diffraction grating (b) for monochromatic light. Maxima can be produced at the same angles, but those for the diffraction grating are narrower, and hence sharper. The maxima become narrower and the regions between become darker as the number of slits is increased.

Diffraction Grating

A CD (compact disc) or DVD
A measuring tape
Sunlight near a white wall

Instructions

Procedure

Hold the CD in direct sunlight near the wall, and move it around until a circular rainbow pattern appears on the wall.
Measure the distance from the CD to the wall and the distance from the center of the circular pattern to a color in the rainbow. Use those two distances to calculate $\tan θ$ . Find $sin θ$ .
Look up the wavelength of the color you chose. That is $λ$ .
Solve $d \sin θ = m λ$ for d.
Compare your answer to the usual spacing between CD tracks, which is 1,600 nm (1.6 μm).
How do you know what number to use for m?
1. Count the rainbow rings preceding the chosen color.
2. Calculate mfrom the frequency of the light of the chosen color.
3. Calculate m from the wavelength of the light of the chosen color.
4. The value of m is fixed for every color.

CD Players

Can you see the grooves on a CD or DVD (see Figure_17_02_CD)? You may think you can because you know they are there, but they are extremely narrow—1,600 in a millimeter. Because the width of the grooves is similar to wavelengths of visible light, they form a diffraction grating. That is why you see rainbows on a CD. The colors are attractive, but they are incidental to the functions of storing and retrieving audio and other data.

View original figure (external; image not reproduced in this text edition)

Original figure description: Drawing of a portable CD player. Its cover is open, showing a CD that has a red sector on the lower left, of about 90 degrees, a blue sector on the upper right of about 120 degrees, and a yellow sector between them of about 30 degrees.

For its size, this CD holds a surprising amount of information. Likewise, the CD player it is in houses a surprising number of electronic devices.

The grooves are actually one continuous groove that spirals outward from the center. Data are recorded in the grooves as binary code (zeroes and ones) in small pits. Information in the pits is detected by a laser that tracks along the groove. It gets even more complicated: The speed of rotation must be varied as the laser tracks toward the circumference so that the linear speed along the groove remains constant. There is also an error correction mechanism to prevent the laser beam from getting off track. A diffraction grating is used to create the first two maxima on either side of the track. If those maxima are not the same distance from the track, an error is indicated and then corrected.

The pits are reflective because they have been coated with a thin layer of aluminum. That allows the laser beam to be reflected back and directed toward a photodiode detector. The signal can then be processed and converted to the audio we hear.

The longest wavelength of visible light is about 780 nm . How does that compare to the distance between CD grooves?

The grooves are about 3 times the longest wavelength of visible light.
The grooves are about 2 times the longest wavelength of visible light.
The grooves are about 2 times the shortest wavelength of visible light.
The grooves are about 3 times the shortest wavelength of visible light.

Biology: DIC Microscopy

If you were completely transparent, it would be hard to recognize you from your photograph. The same problem arises when using a traditional microscope to view or photograph small transparent objects such as cells and microbes. Microscopes using differential interference contrast (DIC) solve the problem by making it possible to view microscopic objects with enhanced contrast, as shown in Figure_17_02_DIC.

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Original figure description: Photo of freshwater alga. A flat green object with a rough texture is divided into forking branches. The largest resembles the letter Y with a very thick stem, tipped to the left so the stem is horizontal. Both arms of the Y fork into two very small branches. Joined to the base of the stem of the Y are other pairs of branches that resemble the letter V, one above and one below, and both angled slightly to the left. Each arm of the V splits into two branches, and then again into very small branches. A mirror image of the Y and two V’s is to the right and the two Y stems are joined.

This aquatic organism was photographed with a DIC microscope. (credit: Public Library of Science)

A DIC microscope separates a polarized light source into two beams polarized at right angles to each other and coherent with each other, that is, in phase. After passing through the sample, the beams are recombined and realigned so they have the same plane of polarization. They then create an interference pattern caused by the differences in their optical path and the refractive indices of the parts of the sample they passed through. The result is an image with contrast and shadowing that could not be observed with traditional optics.

Where are diffraction gratings used? Diffraction gratings are key components of monochromators—devices that separate the various wavelengths of incoming light and allow a beam with only a specific wavelength to pass through. Monochromators are 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 of light emitted by molecules in diseased cells in a biopsy sample, or to help excite strategic molecules in the sample with a selected frequency of light. Another important use is in optical fiber technologies where fibers are designed to provide optimum performance at specific wavelengths. A range of diffraction gratings is available for selecting specific wavelengths for such use.

Diffraction gratings are used in spectroscopes to separate a light source into its component wavelengths. When a material is heated to incandescence, it gives off wavelengths of light characteristic of the chemical makeup of the material. A pure substance will produce a spectrum that is unique, thus allowing identification of the substance. Spectroscopes are also used to measure wavelengths both shorter and longer than visible light. Such instruments have become especially useful to astronomers and chemists. Figure_17_02_Spectroscp shows a diagram of a spectroscope.

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Original figure description: Drawing of a spectroscope. Drawing shows a flame, two mirrors, grating and detector. A yellow flame at the upper left is labeled “source.” A horizontal arrow from the source extends to a small circular arc, which is concave to the left and slightly downward. The arc is one of two that are labeled “mirrors.” A second arrow extends to the left and downward from the point where the first arrow strikes the mirror, and in turn strikes a rectangular object that is tilted from vertical slightly to the left. The object is labeled “grating.” From the point where the second arrow strikes the grating, a number of colored arrows fan out downward and to the right, forming a narrow triangle. Those arrows in turn strike the second circular arc, labeled as one of the “mirrors,” which is concave to the left and slightly upward. From the second mirror, five colored arrows fan out to the left and slightly downward to form a wider triangle, and they strike a vertical surface labeled “detector.” The purple arrow strikes the top of the detector and the blue arrow slightly below it. The green arrow strikes the middle of the detector, the yellow arrow slightly lower, and the red arrow the bottom of the detector.

The diagram shows the function of a diffraction grating in a spectroscope.

Light diffracts as it moves through space, bending around obstacles and interfering constructively and destructively. While diffraction allows light to be used as a spectroscopic tool, it also limits the detail we can obtain in images.

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Figure_17_02_Resolution (a) shows the effect of passing light through a small circular aperture. Instead of a bright spot with sharp edges, a spot with a fuzzy edge surrounded by circles of light is obtained. This pattern is caused by diffraction similar to that produced by a single slit. Light from different parts of the circular aperture interferes constructively and destructively. The effect is most noticeable when the aperture is small, but the effect is there for large apertures, too.

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Original figure description: (a) A white circle on a black background is surrounded by a ring that fades outward from gray to black. (b) Two circles, one on the left and one on the right, are surrounded by gray rings. Their circumferences touch, but the circles are distinguishable. (c)Two circles, with surrounding gray rings, have moved closer together and now are indistinguishable. They form a horizontal oval.

(a) Monochromatic light passed through a small circular aperture produces this diffraction pattern. (b) Two point light sources that are close to one another produce overlapping images because of diffraction. (c) If they are closer together, they cannot be resolved, that is, distinguished.

How does diffraction affect the detail that can be observed when light passes through an aperture? Figure_17_02_Resolution (b) shows the diffraction pattern produced by two point light sources that are close to one another. The pattern is similar to that for a single point source, and it is just barely possible to tell that there are two light sources rather than one. If they are closer together, as in Figure_17_02_Resolution (c), you cannot distinguish them, thus limiting the detail, or resolution, you can obtain. That limit is an inescapable consequence of the wave nature of light.

There are many situations in which diffraction limits the resolution. The acuity of vision is limited because light passes through the pupil, the circular aperture of the eye. Be aware that the diffraction-like spreading of light is due to the limited diameter of a light beam, not the interaction with an aperture. Thus light passing through a lens with a diameter of D shows the diffraction effect and spreads, blurring the image, just as light passing through an aperture of diameter D does. Diffraction limits the resolution of any system having a lens or mirror. Telescopes are also limited by diffraction, because of the finite diameter, D, of their primary mirror.

Calculations Involving Diffraction Gratings and Resolution

Early in the chapter, it was mentioned that when light passes from one medium to another, its speed and wavelength change, but its frequency remains constant. The equation

λ_{n} = \frac{λ}{n}

shows how to the wavelength in a given medium, $λ_{n}$ , is related to the wavelength in a vacuum, $λ$ , and the refractive index, n, of the medium. The equation is useful for calculating the change in wavelength of a monochromatic laser beam in various media. The analysis of a diffraction grating is very similar to that for a double slit. As you know from the discussion of double slits in Young’s double-slit experiment, light is diffracted by, and spreads out after passing through, each slit. Rays travel at an angle $θ$ relative to the incident direction. Each ray travels a different distance to a common point on a screen far away. The rays start in phase, and they can be in or out of phase when they reach a screen, depending on the difference in the path lengths traveled. Each ray travels a distance that differs by $d \sin θ$ from that of its neighbor, where d is the distance between slits. If $d \sin θ$ equals an integral number of wavelengths, the rays all arrive in phase, and constructive interference (a maximum) is obtained. Thus, the condition necessary to obtain constructive interference for a diffraction grating is

d \sin θ = m λ, for m = 0, 1, - 1, 2, - 2, \dots,

where d is the distance between slits in the grating, $λ$ is the wavelength of the light, and m is the order of the maximum. Note that this is exactly the same equation as for two slits separated by d. However, the slits are usually closer in diffraction gratings than in double slits, producing fewer maxima at larger angles.

Just what is the resolution limit of an aperture or lens? To answer that question, consider the diffraction pattern for a circular aperture, which, similar to the diffraction pattern of light passing through a slit, has a central maximum that is wider and brighter than the maxima surrounding it (see Figure_17_02_Resolution (a)). It can be shown that, for a circular aperture of diameter D, the first minimum in the diffraction pattern occurs at $θ = 1.22 λ / D$ , provided that the aperture is large compared with the wavelength of light, which is the case for most optical instruments. The accepted criterion for determining the diffraction limit to resolution based on diffraction was developed by Lord Rayleigh in the 19th century. The Rayleigh criterion for the diffraction limit to resolution states that two images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other. See Figure_17_02_Resolution2 (b). The first minimum is at an angle of $θ = 1.22 λ / D$ , so that two point objects are just resolvable if they are separated by the angle

θ = 1.22 \frac{λ}{D},

where $λ$ is the wavelength of the light (or other electromagnetic radiation) and D is the diameter of the aperture, lens, mirror, etc., with which the two objects are observed. In the expression above, $θ$ has units of radians.

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Original figure description: (a) A graph with five peaks. The valleys are on a horizontal axis. The central peak is largest, and it is labeled “intensity.” Four much smaller peaks are arranged symmetrically, two to the left and two to the right. An arrow below the horizontal axis points to the right and is labeled “theta.” Three points are labeled on the horizontal axis, “zero” for the central peak, “negative 1.22 lamda divided by D” for the valley on its left, and “1.22 lamda divided by D” for the valley on its right. (b) A drawing shows two lightbulbs at the bottom. One is labeled “Object 1,” and it is to the right and slightly above the other, labeled “Object 2.” In the middle of the drawing is a vertical screen with a circular hole in it. At the top of the drawing is a vertical screen with two wide peaks graphed on it, which are labeled “Intensities.” A line from Object 1 extends through the hole in the screen and strikes the horizontal axis of the graph directly below the left peak on the graph. Another line from Object two extends through the hole in the screen and strikes the horizontal axis of the graph directly below the right peak on the graph. The angle formed when the two lines cross (where they pass through the hole in the middle screen) is labeled “theta min.”

(a) Graph of intensity of the diffraction pattern for a circular aperture. Note that, similar to a single slit, the central maximum is wider and brighter than those to the sides. (b) Two point objects produce overlapping diffraction patterns. Shown here is the Rayleigh criterion for their being just resolvable. The central maximum of one pattern lies on the first minimum of the other.

Diffraction Grating

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

Solution

First find d.

d = \frac{1 cm}{2,000} = 5.00 \times 10^{- 4} cm = 5,000 nm

Rearrange the equation for constructive interference conditions for a diffraction grating, and substitute the known values.

$\begin{matrix} d \sin θ & = & m λ \\ θ & = & {sin}^{- 1} \frac{m λ}{d} \\ = & {sin}^{- 1} (\frac{(1) (520)}{5,000}) \\ = & 5.97 \end{matrix}$

Discussion

This angle seems reasonable for the first maximum. Recall that the meaning of sin^‒1 (or arcsin) is the angle with a sine that is (the unknown). Remember that the value of $\sin θ$ will not be greater than 1 for any value of $θ$ .

Practice Problems

A beam of yellow light has a wavelength of 600 nm in a vacuum and a wavelength of 397 nm in Plexiglas. What is the refractive index of Plexiglas?

1.51
2.61
3.02
3.77

What is the angle between two just-resolved points of light for a 3.00 mm diameter pupil, assuming an average wavelength of 550 nm?

224 rad
183 rad
1.83 × 10^–4 rad
2.24 × 10^–4 rad

Check Your Understanding

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Section Summary

The focused, coherent radiation emitted by lasers has many uses in medicine and industry.
Characteristics of diffraction patterns produced with diffraction gratings can be determined.
Diffraction gratings have been incorporated in many instruments, including microscopes and spectrometers.
Resolution has a limit that can be predicted.

Key Equations

wavelength change with change in medium	$λ_{n} = \frac{λ}{n}$
diffraction grating constructive interference	$d \sin θ = m λ$
resolution	$θ = 1.22 \frac{λ}{D}$

Concept Items

There is a principle related to resolution that is expressed by this equation.

θ = \frac{λ}{D}

What is that principle stated in full?

A principle related to resolution states, “Two images are just resolved when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.” Write the equation that expresses that principle.

$θ = 1.22 \frac{D}{λ}$
$θ = \frac{D}{λ}$
$θ = \frac{λ}{D}$
$θ = 1.22 \frac{λ}{D}$

Which statement completes this resolution?
Two images are just resolved when —

The center of the diffraction pattern of one image is directly over the central maximum of the diffraction pattern of the other.
The center of the diffraction pattern of one image is directly over the central minimum of the diffraction pattern of the other
The center of the diffraction pattern of one image is directly over the first minimum of the diffraction pattern of the other
The center of the diffraction pattern of one is directly over the first maximum of the diffraction pattern of the other

Critical Thinking

For what type of electromagnetic radiation would a grating with spacing greater than 800 nm be useful as a spectroscopic tool?

It can be used to analyze spectra only in the infrared portion of the spectrum.
It can be used to analyze spectra in the entire visible portion of the electromagnetic spectrum.
It can only be used to analyze spectra in the short‐wavelength visible.
It can only be used to analyze spectra in the short‐wavelength visible and ultraviolet.

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Problems

A 500-nm beam of light passing through a diffraction grating creates its second band of constructive interference at an angle of 1.50°. How far apart are the slits in the grating?

38,200 nm
19,100 nm
667 nm
333 nm

The range of the visible-light spectrum is 380 nm to 780 nm. What is the maximum number of lines per centimeter a diffraction grating can have and produce a complete first-order spectrum for visible light?

26,300 lines/cm
13,200 lines/cm
6,410 lines/cm
12,820 lines/cm

Test Prep Multiple Choice

Two images are just resolved when the center of the diffraction pattern of one is directly over ________ of the diffraction pattern of the other.

the center
the first minimum
the first maximum
the last maximum

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Will a beam of light shining through a 1-mm hole behave any differently than a beam of light that is 1 mm wide as it leaves its source? Explain.?

Yes, the beam passing through the hole will spread out as it travels, because it is diffracted by the edges of the hole, whereas the 1 -mm beam, which encounters no diffracting obstacle, will not spread out.
Yes, the beam passing through the hole will be made more parallel by passing through the hole, and so will not spread out as it travels, whereas the unaltered wavefronts of the 1-mm beam will cause the beam to spread out as it travels.
No, both beams will remain the same width as they travel, and they will not spread out.
No, both beams will spread out as they travel.

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Test Prep Short Answer

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Suppose pure-wavelength light falls on a diffraction grating. What happens to the interference pattern if the same light falls on a grating that has more lines per centimeter?

The bands will spread farther from the central maximum.
The bands will come closer to the central maximum.
The bands will not spread farther from the first maximum.
The bands will come closer to the first maximum.

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 473 nm blue light at an angle of 25.0°?

529,000 lines/cm
50,000 lines/cm
851 lines/cm
8,934 lines/cm

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 60.0°?

2.28 × 10⁴ nm
3.29 × 10² nm
2.53 × 10¹ nm
1.76 × 10³ nm

Extended Response

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Performance Task

In this performance task you will create one- and two-slit diffraction and observe the interference patterns that result.

A utility knife (a knife with a razor blade-like cutting edge)
Aluminum foil
A straight edge
A strong, small light source or a laser pointer
A tape measure
A white wall

Procedure

Cut a piece of aluminum foil about 15 cm × 15 cm.
Use the utility knife and the straight edge to cut a straight slit several cm long in the center of the foil square.
With the room darkened, one partner shines the light through the slit and toward the wall. The other partner observes the pattern on the wall. The partner with the light changes the distance from the foil to the wall and the distance from the light to the foil.
When the sharpest, brightest pattern possible is obtained, the partner who is not holding the foil and light makes measurements.
Measure the perpendicular (shortest) distance from the slit to the wall, the distance from the center of the pattern to several of the dark bands, and the distance from the slit to the same dark bands.
Carefully make a second slit parallel to the first slit and 1 mm or less away.
Repeat steps 2 through 5, only this time measure the distances to bright bands.
NOTE—In your calculations, use 580 nm for $λ$ if you used white light. If you used a colored laser pointer, look up the wavelength of the color. You may find it easier to calculate $θ$ from its tangent rather than from its sine.
1. Which experiment gave the most distinct pattern—one or two slits?
2. What was the width of the single slit? Compare the calculated distance with the measured distance.
3. What was the distance between the two slits? Compare the calculated distance with the measured distance.

Teacher Support

This performance task supports NGSS HS-PS4-3: Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other.

Clarification Statement—Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect.

Assessment Boundary—Assessment does not include using quantum theory.

AND

S&EP—Use mathematical representations of phenomena or design solutions to describe and/or support claims and/or explanations.

The double-slit pattern was more distinct.
Answers will vary. Calculation should employ $D \sin θ = m λ$ or $\frac{D y}{L} = m λ$ .
Answers will vary. Calculation should employ $d \sin θ = m λ$ .

Glossary

diffraction grating: many of evenly spaced slits having dimensions such that they produce an interference pattern
differential interference contrast (DIC): separating a polarized light source into two beams polarized at right angles to each other and coherent with each other then, after passing through the sample, recombining and realigning the beams so they have the same plane of polarization, and then creating an interference pattern caused by the differences in their optical path and the refractive indices of the parts of the sample they passed through; the result is an image with contrast and shadowing that could not be observed with traditional optics
iridescence: the effect that occurs when tiny, fingerlike structures in regular patterns act as reflection gratings, producing constructive interference that gives feathers colors not solely due to their pigmentation
laser: acronym for a device that produces light amplification by stimulated emission of radiation
monochromator: device that separates the various wavelengths of incoming light and allows a beam with only a specific wavelength to pass through
Rayleigh criterion: two images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other
resolution: degree to which two images can be distinguished from one another, which is limited by diffraction

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