# Diffraction - Fundamentals, Applications

### aperture light pattern waves

Diffraction is the deviation from a straight path that occurs when a wave such as light or sound passes around an obstacle or through an opening. The importance of diffraction in any particular situation depends on the relative size of the obstacle or opening and the wavelength of the wave that strikes it. The diffraction grating is an important device that makes use of the diffraction of light to produce spectra. Diffraction is also fundamental in other applications such as x-ray diffraction studies of crystals and holography.

All waves are subject to diffraction when they encounter an obstacle in their path. Consider the shadow of a flagpole cast by the Sun on the ground. From a distance the darkened zone of the shadow gives the impression that light traveling in a straight line from the Sun was blocked by the pole. But careful observation of the shadow's edge will reveal that the change from dark to light is not abrupt. Instead, there is a gray area along the edge that was created by light that was "bent" or diffracted at the side of the pole.

When a source of waves, such as a light bulb, sends a beam through an opening or aperture, a diffraction pattern will appear on a screen placed behind the aperture. The diffraction pattern will look something like the aperture (a slit, circle, square) but it will be surrounded by some diffracted waves that give it a "fuzzy" appearance.

If both the source and the screen are far from the aperture the amount of "fuzziness" is determined by the wavelength of the source and the size of the aperture. With a large aperture most of the beam will pass straight through, with only the edges of the aperture causing diffraction, and there will be less "fuzziness." But if the size of the aperture is comparable to the wavelength, the diffraction pattern will widen. For example, an open window can cause sound waves to be diffracted through large angles.

Fresnel diffraction refers to the case when either the source or the screen are close to the aperture. When both source and screen are far from the aperture, the term Fraunhofer diffraction is used. As an example of the latter, consider starlight entering a telescope. The diffraction pattern of the telescope's circular mirror or lens is known as Airy's disk, which is seen as a bright central disk in the middle of a number of fainter rings. This indicates that the image of a star will always be widened by diffraction. When optical instruments such as telescopes have no defects, the greatest detail they can observe is said to be diffraction limited.

### Diffraction gratings

The diffraction of light has been cleverly taken advantage of to produce one of science's most important tools—the diffraction grating. Instead of just one aperture, a large number of thin slits or grooves—as many as 25,000 per inch—are etched into a material. In making these sensitive devices it is important that the grooves are parallel, equally spaced, and have equal widths.

The diffraction grating transforms an incident beam of light into a spectrum. This happens because each groove of the grating diffracts the beam, but because all the grooves are parallel, equally spaced and have the same width, the diffracted waves mix or interfere constructively so that the different components can be viewed separately. Spectra produced by diffraction gratings are extremely useful in applications from studying the structure of atoms and molecules to investigating the composition of stars.

### X-ray diffraction

X rays are light waves that have very short wavelengths. When they irradiate a solid, crystal material they are diffracted by the atoms in the crystal. But since it is a characteristic of crystals to be made up of equally spaced atoms, it is possible to use the diffraction patterns that are produced to determine the locations and distances between atoms. Simple crystals made up of equally spaced planes of atoms diffract x rays according to Bragg's Law. Current research using x-ray diffraction utilizes an instrument called a diffractometer to produce diffraction patterns that can be compared with those of known crystals to determine the structure of new materials.

### Holography

When two laser beams mix at an angle on the surface of a photographic plate or other recording material, they produce an interference pattern of alternating dark and bright lines. Because the lines are perfectly parallel, equally spaced, and of equal width, this process is used to manufacture holographic diffraction gratings of high quality. In fact, any hologram (holos—whole: gram—message) can be thought of as a complicated diffraction grating. The recording of a hologram involves the mixing of a laser beam and the unfocused diffraction pattern of some object. In order to reconstruct an image of the object (holography is also known as wavefront reconstruction) an illuminating beam is diffracted by plane surfaces within the hologram, following Bragg's Law, such that an observer can view the image with all of its three-dimensional detail.

John Appel

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Airy's disk

—The diffraction pattern produced by a circular aperture such as a lens or a mirror.

Bragg's law

—An equation that describes the diffraction of light from plane parallel surfaces.

Diffraction limited

—The ultimate performance of an optical element such as a lens or mirror that depends only on the element's finite size.

Diffraction pattern

—The wave pattern observed after a wave has passed through a diffracting aperture.

Diffractometer

—A device used to produce diffraction patterns of materials.

Fresnel diffraction

—Diffraction that occurs when the source and the observer are far from the diffraction aperture.

Interference pattern

—Alternating bands of light and dark that result from the mixing of two waves.

Wavelength

—The distance between two consecutive crests or troughs in a wave.

X-ray diffraction

—A method using the scattering of x rays by matter to study the structure of crystals.

Diffraction Grating [next]

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can i know about applications of diffraction.

almost 5 years ago

use for spectrum analysis. diffracted light use in operation theater. it can also to find refractive index.use in definding the structure of crystal.

over 3 years ago

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