DIFFRACTION

CONCEPT

Diffraction is the bending of waves around obstacles, or the spreading of waves by passing them through an aperture, or opening. Any type of energy that travels in a wave is capable of diffraction, and the diffraction of sound and light waves produces a number of effects. (Because sound waves are much larger than light waves, however, diffraction of sound is a part of daily life that most people take for granted.) Diffraction of light waves, on the other hand, is much more complicated, and has a number of applications in science and technology, including the use of diffraction gratings in the production of holograms.

HOW IT WORKS

Comparing Sound and Light Diffraction

Imagine going to a concert hall to hear a band, and to your chagrin, you discover that your seat is directly behind a wide post. You cannot see the band, of course, because the light waves from the stage are blocked. But you have little trouble hearing the music, since sound waves simply diffract around the pillar. Light waves diffract slightly in such a situation, but not enough to make a difference with regard to your enjoyment of the concert: if you looked closely while sitting behind the post, you would be able to observe the diffraction of the light waves glowing slightly, as they widened around the post.

Suppose, now, that you had failed to obtain a ticket, but a friend who worked at the concert venue arranged to let you stand outside an open door and hear the band. The sound quality would be far from perfect, of course, but you would still be able to hear the music well enough. And if you stood right in front of the doorway, you would be able to see light from inside the concert hall. But, if you moved away from the door and stood with your back to the building, you would see little light, whereas the sound would still be easily audible.

WAVELENGTH AND DIFFRACTION.

The reason for the difference—that is, why sound diffraction is more pronounced than light diffraction—is that sound waves are much, much larger than light waves. Sound travels by longitudinal waves, or waves in which the movement of vibration is in the same direction as the wave itself. Longitudinal waves radiate outward in concentric circles, rather like the rings of a bull's-eye.

The waves by which sound is transmitted are larger, or comparable in size to, the column or the door—which is an example of an aperture—and, hence, they pass easily through apertures and around obstacles. Light waves, on the other hand, have a wavelength, typically measured in nanometers (nm), which are equal to one-millionth of a millimeter. Wavelengths for visible light range from 400 (violet) to 700 nm (red): hence, it would be possible to fit about 5,000 of even the longest visible-light wavelengths on the head of a pin!

Whereas differing wavelengths in light are manifested as differing colors, a change in sound wavelength indicates a change in pitch. The higher the pitch, the greater the frequency, and, hence, the shorter the wavelength. As with light waves—though, of course, to a much lesser extent—short-wavelength sound waves are less capable of diffracting around large objects than are long-wave length sound waves. Chances are, then, that the most easily audible sounds from inside the concert hall are the bass and drums; higher-pitched notes from a guitar or other instruments, such as a Hammond organ, are not as likely to reach a listener outside.

Observing Diffraction in Light

Due to the much wider range of areas in which light diffraction has been applied by scientists, diffraction of light and not sound will be the principal topic for the remainder of this essay. We have already seen that wavelength plays a role in diffraction; so, too, does the size of the aperture relative to the wavelength. Hence, most studies of diffraction in light involve very small openings, as, for instance, in the diffraction grating discussed below.

But light does not only diffract when passing through an aperture, such as the concert-hall door in the earlier illustration; it also diffracts around obstacles, as, for instance, the post or pillar mentioned earlier. This can be observed by looking closely at the shadow of a flagpole on a bright morning. At first, it appears that the shadow is "solid," but if one looks closely enough, it becomes clear that, at the edges, there is a blurring from darkness to light. This "gray area" is an example of light diffraction.

Where the aperture or obstruction is large compared to the wave passing through or around it, there is only a little "fuzziness" at the edge, as in the case of the flagpole. When light passes through an aperture, most of the beam goes straight through without disturbance, with only the edges experiencing diffraction. If, however, the size of the aperture is close to that of the wavelength, the diffraction pattern will widen. Sound waves diffract at large angles through an open door, which, as noted, is comparable in size to a sound wave; similarly, when light is passed through extremely narrow openings, its diffraction is more noticeable.

Early Studies in Diffraction

Though his greatest contributions lay in his epochal studies of gravitation and motion, Sir Isaac Newton (1642-1727) also studied the production and propagation of light. Using a prism, he separated the colors of the visible light spectrum—something that had already been done by other scientists—but it was Newton who discerned that the colors of the spectrum could be recombined to form white light again.

Newton also became embroiled in a debate as the nature of light itself—a debate in which diffraction studies played an important role. Newton's view, known at the time as the corpuscular theory of light, was that light travels as a stream of particles. Yet, his contemporary, Dutch physicist and astronomer Christiaan Huygens (1629-1695), advanced the wave theory, or the idea that light travels by means of waves. Huygens maintained that a number of factors, including the phenomena of reflection and refraction, indicate that light is a wave. Newton, on the other hand, challenged wave theorists by stating that if light were actually a wave, it should be able to bend around corners—in other words, to diffract.

GRIMALDI IDENTIFIES DIFFRACTION.

Though it did not become widely known until some time later, in 1648—more than a decade before the particle-wave controversy erupted—Johannes Marcus von Kronland (1595-1667), a scientist in Bohemia (now part of the Czech Republic), discovered the diffraction of light waves. However, his findings were not recognized until some time later; nor did he give a name to the phenomenon he had observed. Then, in 1660, Italian physicist Francesco Grimaldi (1618-1663) conducted an experiment with diffraction that gained widespread attention.

Grimaldi allowed a beam of light to pass through two narrow apertures, one behind the other, and then onto a blank surface. When he did so, he observed that the band of light hitting the surface was slightly wider than it should be, based on the width of the ray that entered the first aperture. He concluded that the beam had been bent slightly outward, and gave this phenomenon the name by which it is known today: diffraction.

FRESNEL AND FRAUNHOFER DIFFRACTION.

Particle theory continued to have its adherents in England, Newton's homeland, but by the time of French physicist Augustin Jean Fresnel (1788-1827), an increasing number of scientists on the European continent had come to accept the wave theory. Fresnel's work, which he published in 1818, served to advance that theory, and, in particular, the idea of light as a transverse wave.

In Memoire sur la diffraction de la lumiere, Fresnel showed that the transverse-wave model accounted for a number of phenomena, including diffraction, reflection, refraction, interference, and polarization, or a change in the oscillation patterns of a light wave. Four years after publishing this important work, Fresnel put his ideas into action, using the transverse model to create a pencil-beam of light that was ideal for lighthouses. This prism system, whereby all the light emitted from a source is refracted into a horizontal beam, replaced the older method of mirrors used since ancient times. Thus Fresnel's work revolutionized the effectiveness of lighthouses, and helped save lives of countless sailors at sea.

The term "Fresnel diffraction" refers to a situation in which the light source or the screen are close to the aperture; but there are situations in which source, aperture, and screen (or at least two of the three) are widely separated. This is known as Fraunhofer diffraction, after German physicist Joseph von Fraunhofer (1787-1826), who in 1814 discovered the lines of the solar spectrum (source) while using a prism (aperture). His work had an enormous impact in the area of spectroscopy, or studies of the interaction between electromagnetic radiation and matter.

REAL-LIFE APPLICATIONS

Diffraction Studies Come of Age

Eventually the work of Scottish physicist James Clerk Maxwell (1831-1879), German physicist Heinrich Rudolf Hertz (1857-1894), and others confirmed that light did indeed travel in waves. Later, however, Albert Einstein (1879-1955) showed that light behaves both as a wave and, in certain circumstances, as a particle.

In 1912, a few years after Einstein published his findings, German physicist Max Theodor Felix von Laue (1879-1960) created a diffraction grating, discussed below. Using crystals in his grating, he proved that x rays are part of the electromagnetic spectrum. Laue's work, which earned him the Nobel Prize in physics in 1914, also made it possible to measure the length of x rays, and, ultimately, provided a means for studying the atomic structure of crystals and polymers.

SCIENTIFIC BREAKTHROUGHS MADE POSSIBLE BY DIFFRACTION STUDIES.

Studies in diffraction advanced during the early twentieth century. In 1926, English physicist J. D. Bernal (1901-1971) developed the Bernal chart, enabling scientists to deduce the crystal structure of a solid by analyzing photographs of x-ray diffraction patterns. A decade later, Dutch-American physical chemist Peter Joseph William Debye (1884-1966) won the Nobel Prize in Chemistry for his studies in the diffraction of x rays and electrons in gases, which advanced understanding of molecular structure. In 1937, a year after Debye's Nobel, two other scientists—American physicist Clinton Joseph Davisson (1881-1958) and English physicist George Paget Thomson (1892-1975)—won the Prize in Physics for their discovery that crystals can bring about the diffraction of electrons.

Also, in 1937, English physicist William Thomas Astbury (1898-1961) used x-ray diffraction to discover the first information concerning nucleic acid, which led to advances in the study of DNA (deoxyribonucleic acid), the building-blocks of human genetics. In 1952, English biophysicist Maurice Hugh Frederick Wilkins (1916-) and molecular biologist Rosalind Elsie Franklin (1920-1958) used x-ray diffraction to photograph DNA. Their work directly influenced a breakthrough event that followed a year later: the discovery of the double-helix or double-spiral model of DNA by American molecular biologists James D. Watson (1928-) and Francis Crick (1916-). Today, studies in DNA are at the frontiers of research in biology and related fields.

Diffraction Grating

Much of the work described in the preceding paragraphs made use of a diffraction grating, first developed in the 1870s by American physicist Henry Augustus Rowland (1848-1901). A diffraction grating is an optical device that consists of not one but many thousands of apertures: Rowland's machine used a fine diamond point to rule glass gratings, with about 15,000 lines per in (2.2 cm). Diffraction gratings today can have as many as 100,000 apertures per inch. The apertures in a diffraction grating are not mere holes, but extremely narrow parallel slits that transform a beam of light into a spectrum.

Each of these openings diffracts the light beam, but because they are evenly spaced and the same in width, the diffracted waves experience constructive interference. (The latter phenomenon, which describes a situation in which two or more waves combine to produce a wave of greater magnitude than either, is discussed in the essay on Interference.) This constructive interference pattern makes it possible to view components of the spectrum separately, thus enabling a scientist to observe characteristics ranging from the structure of atoms and molecules to the chemical composition of stars.

X-RAY DIFFRACTION.

Because they are much higher in frequency and energy levels, x rays are even shorter in wavelength than visible light waves. Hence, for x-ray diffraction, it is necessary to have gratings in which lines are separated by infinitesimal distances. These distances are typically measured in units called an angstrom, of which there are 10 million to a millimeter. Angstroms are used in measuring atoms, and, indeed, the spaces between lines in an x-ray diffraction grating are comparable to the size of atoms.

When x rays irradiate a crystal—in other words, when the crystal absorbs radiation in the form of x rays—atoms in the crystal diffract the rays. One of the characteristics of a crystal is that its atoms are equally spaced, and, because of this, it is possible to discover the location and distance between atoms by studying x-ray diffraction patterns. Bragg's law—named after the father-andson team of English physicists William Henry Bragg (1862-1942) and William Lawrence Bragg (1890-1971)—describes x-ray diffraction patterns in crystals.

Though much about x-ray diffraction and crystallography seems rather abstract, its application in areas such as DNA research indicates that it has numerous applications for improving human life. The elder Bragg expressed this fact in 1915, the year he and his son received the Nobel Prize in physics, saying that "We are now able to look ten thousand times deeper into the structure of the matter that makes up our universe than when we had to depend on the microscope alone." Today, physicists applying x-ray diffraction use an instrument called a diffractometer, which helps them compare diffraction patterns with those of known crystals, as a means of determining the structure of new materials.

Holograms

A hologram—a word derived from the Greek holos, "whole," and gram, "message"—is a three-dimensional (3-D) impression of an object, and the method of producing these images is known as holography. Holograms make use of laser beams that mix at an angle, producing an interference pattern of alternating bright and dark lines. The surface of the hologram itself is a sort of diffraction grating, with alternating strips of clear and opaque material. By mixing a laser beam and the unfocused diffraction pattern of an object, an image can be recorded. An illuminating laser beam is diffracted at specific angles, in accordance with Bragg's law, on the surfaces of the hologram, making it possible for an observer to see a three-dimensional image.

Holograms are not to be confused with ordinary three-dimensional images that use only visible light. The latter are produced by a method known as stereoscopy, which creates a single image from two, superimposing the images to create the impression of a picture with depth. Though stereoscopic images make it seem as though one can "step into" the picture, a hologram actually enables the viewer to glimpse the image from any angle. Thus, stereoscopic images can be compared to looking through the plate-glass window of a store display, whereas holograms convey the sensation that one has actually stepped into the store window itself.

DEVELOPMENTS IN HOLOGRAPHY.

While attempting to improve the resolution of electron microscopes in 1947, Hungarian-English physicist and engineer Dennis Gabor (1900-1979) developed the concept of holography and coined the term "hologram." His work in this area could not progress by a great measure, however, until the creation of the laser in 1960. By the early 1960s, scientists were using lasers to create 3-D images, and in 1971, Gabor received the Nobel Prize in physics for the discovery he had made a generation before.

Today, holograms are used on credit cards or other identification cards as a security measure, providing an image that can be read by an optical scanner. Supermarket checkout scanners use holographic optical elements (HOEs), which can read a universal product code (UPC) from any angle. Use of holograms in daily life and scientific research is likely to increase as scientists find new applications: for instance, holographic images will aid the design of everything from bridges to automobiles.

HOLOGRAPHIC MEMORY.

One of the most fascinating areas of research in the field of holography is holographic memory. Computers use a binary code, a pattern of ones and zeroes that is translated into an electronic pulse, but holographic memory would greatly extend the capabilities of computer memory systems. Unlike most images, a hologram is not simply the sum of its constituent parts: the data in a holo-graphic image is contained in every part of the image, meaning that part of the image can be destroyed without a loss of data.

To bring the story full-circle, holographic memory calls to mind an idea advanced by a scientist who, along with Huygens, was one of Newton's great professional rivals, German mathematician and philosopher Gottfried Wilhelm Leibniz (1646-1716). Though Newton is usually credited as the father of calculus, Leibniz developed his own version of calculus at around the same time.

As a philosopher, Leibniz had apparently had a number of strange ideas, which made him the butt of jokes among some sectors of European intellectual society: hence, the French writer and thinker Voltaire (François-Marie Arouet; 1694-1778) satirized him with the character Dr. Pangloss in Candide (1759). Few of Leibniz's ideas were more bizarre than that of the monad: an elementary particle of existence that reflected the whole of the universe.

In advancing the concept of a monad, Leibniz was not making a statement after the manner of a scientist: there was no proof that monads existed, nor was it possible to prove this in any scientific way. Yet, a hologram appears to be very much like a manifestation of Leibniz's imagined monads, and both the hologram and the monad relate to a more fundamental aspect of life: human memory. Neurological research in the late twentieth century suggested that the structure of memory in the human mind is holo-graphic. Thus, for instance, a patient suffering an injury affecting 90% of the brain experiences only a 10% memory loss.

WHERE TO LEARN MORE

Barrett, Norman S. Lasers and Holograms. New York: F. Watts, 1985.

"Bragg's Law and Diffraction: How Waves Reveal the Atomic Structure of Crystals" (Web site). <http://www.journey.sunysb.edu/ProjectJava/Bragg/home.html> (May 6, 2001).

Burkig, Valerie. Photonics: The New Science of Light. Hillside, N.J.: Enslow Publishers, 1986.

"Diffraction of Sound" (Web site). <http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html> (May 6, 2001).

Gardner, Robert. Experimenting with Light. New York: F. Watts, 1991.

Graham, Ian. Lasers and Holograms. New York: Shooting Star Press, 1993.

Holoworld: Holography, Lasers, and Holograms (Web site). <http://www.holoworld.com> (May 6, 2001).

Proffen, T. H. and R. B. Neder. Interactive Tutorial About Diffraction (Web site). <http://www.uniwuerzburg.de/mineralogie/crystal/teaching/teaching.html> (May 6, 2001).

Snedden, Robert. Light and Sound. Des Plaines, IL: Heinemann Library, 1999.

"Wave-Like Behaviors of Light." The Physics Classroom (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/u12l1a.html> (May 6, 2001).

KEY TERMS

APERTURE:

An opening.

DIFFRACTION:

The bending of waves around obstacles, or the spreading of waves by passing them through an aperture.

ELECTROMAGNETIC SPECTRUM:

The complete range of electromagnetic waves on a continuous distribution from a very low range of frequencies and energylevels, with a correspondingly long wavelength, to a very high range of frequencies and energy levels, with a correspondingly short wavelength. Included on the electromagnetic spectrum are long-wave and short-wave radio; microwaves; infrared, visible, and ultraviolet light; x rays, and gamma rays.

FREQUENCY:

The number of waves passing through a given point during the interval of one second. The higher the frequency, the shorter the wavelength.

LONGITUDINAL WAVE:

A wave in which the movement of vibration is in the same direction as the wave itself. A sound wave is an example of a longitudinal wave.

PRISM:

A three-dimensional glassshape used for the diffusion of light rays.

PROPAGATION:

The act or state of traveling from one place to another.

RADIATION:

In a general sense, radiation can refer to anything that travels in astream, whether that stream be composed of subatomic particles or electromagnetic waves.

REFLECTION:

A phenomenon whereby a light ray is returned toward its source rather than being absorbed at the interface.

REFRACTION:

The bending of a lightray that occurs when it passes through a dense medium, such as water or glass.

SPECTRUM:

The continuous distribution of properties in an ordered arrangement across an unbroken range. Examples of spectra (the plural of "spectrum") include the colors of visible light, or the electromagnetic spectrum of which visiblelight is a part.

TRANSVERSE WAVE:

A wave in which the vibration or motion is perpendicular to the direction in which the wave is moving.

WAVELENGTH:

The distance between a crest and the adjacent crest, or the trough and an adjacent trough, of a wave. The shorter the wavelength, the higher the frequency.

Diffraction

Fundamentals

Applications

Diffraction is the deviation of a traveling wave (light, sound, or other) from a straight path that occurs when the wave passes around an obstacle or through an opening. The importance of diffraction in any given situation depends on the relative size of the obstacle or opening and the wavelength of the wave striking it. The diffraction grating is an important device that uses the diffraction of light to produce spectra, that is, to spatially separate mixed light into its frequency components so that they can be measured independently. Diffraction is also fundamental in other applications such as x-ray diffraction studies of crystals and holography.

Fundamentals

All waves are subject to diffraction when they encounter an obstacle. 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. Moreover, the edge of the pole’s shadow grows fuzzier as one traces it from the base to the tip; the farther the shadow from the shadow-casting object, the more pronounced the diffraction.

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 source and 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.

Applications

Diffraction gratings

The diffraction of light has been taken advantage of to produce one of science’s most useful 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.

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.

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, 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.

See also Hologram and holography; Wave motion.

John Appel

Diffraction

Diffraction is the bending of waves (such as light waves or sound waves) as they pass around an obstacle or through an opening. Anyone who has watched ocean waves entering a bay or harbor has probably witnessed diffraction. As the waves strike the first point of land, they change direction. Instead of moving into the bay or harbor parallel to (in the same direction as) land, they travel at an angle to it. The narrower the opening, the more dramatic the effect. As waves enter a narrow harbor opening, such as San Francisco's Golden Gate, they change from a parallel set of wave fronts to a fan-shaped pattern.

The diffraction of light has many important applications. For example, a device known as the diffraction grating is used to break white light apart into its colored components. Patterns produced by diffraction gratings provide information about the kind of light that falls on them.

Fundamentals

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 lightbulb, 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 (perhaps a slit, a circle, or a square) but it will be surrounded by some diffracted waves that give it a fuzzy appearance.

The diffraction that occurs depends primarily on two variables: the wavelength of the wave and the size of the opening or aperture through which the waves pass. (Wavelength is defined as the distance between two identical parts of a wave, such as two consecutive crests of a wave. The only difference between waves of light, waves of radar, waves of X rays, and of many other kinds of waves is their wavelength—and their frequency, which depends on their wavelength.) The wavelength of light, for example, is in the range of 400 to 700 nanometers (billionths of a meter). In comparison, the wavelength of radar waves ranges from about 0.1 to 1 meter.

Words to Know

Diffraction pattern: The wave pattern observed after a wave has passed through a diffracting aperture (or opening).

Frequency: The number of segments in a wave that pass a given point every second.

Interference pattern: Alternating bands of light and dark that result from the mixing of two waves.

Wavelength: The distance between two identical parts of a wave, such as two consecutive crests of the wave.

X-ray diffraction: A method used for studying the structure of crystals.

When the wavelength of a wave is much smaller than the aperture through which it travels, the observed diffraction is small. A beam of light traveling through a window, for example, has a wavelength many trillions of times smaller than the window opening. It would be difficult to observe diffraction in this situation. But a beam of light passing through a tiny pin hole produces a different effect. In this case, a diffraction pattern can be seen quite clearly.

Applications

Diffraction gratings. A diffraction grating is a tool whose operation is based on the diffraction of light. It consists of a flat plate (usually made of glass or plastic) into which are etched thousands of thin slits or grooves. The accuracy of the grating depends on the grooves' being parallel to each other, equally spaced, and equal in width.

When light strikes a diffraction grating, it is diffracted by each of the thousands of grooves individually. The diffracted waves that are produced then mix or interfere with each other in different ways, depending on the source of the light beam. Light from a sodium vapor lamp, from a mercury (fluorescent) lamp, and from an incandescent lamp all produce different light patterns in a diffraction grating.

Scientists have recorded the kind of light pattern (spectrum) produced when each of the different chemical elements is heated and its light shined on a diffraction grating. In studying the light of an unknown object (such as a star), then, the diffraction grating spectrum can be compared to the known spectra of elements. In this way, elements in the unknown object can be identified.

X-ray diffraction. In the 1910s, William Henry (1862–1942) and William Lawrence Bragg (1890–1971), a father-and-son team of English physicists, had an interesting idea for using diffraction. They set out to find the very finest diffraction grating anyone could imagine and decided that a crystal—such as a crystal of ordinary table salt—fit the bill. The atoms and ions that make up a crystal are arranged in the same way as the grooves of a diffraction grating. Crystalline atoms and ions are laid out in very orderly rows at exactly the same distance from each other, as is the case with a diffraction grating. But the size of the "grooves" in a crystal (the space between atoms and ions) is much smaller than in any human-made diffraction grating.

The Braggs set to work experimenting with crystals and diffraction. Unfortunately, the wavelength of a light wave was too large to be diffracted by atoms and ions in a crystal. But X rays—which have a much smaller wavelength than light waves—would diffract perfectly off rows of atoms or ions in a crystal.

When the Braggs shined X rays off various crystals, they made a fascinating discovery. For each type of crystal studied, a unique pattern of fuzzy circles was produced. X rays had been diffracted according to the ways in which atoms or ions were arranged in the crystal. The Braggs had discovered a method for determining how atoms or ions are arranged in a given crystal. That method, known as X-ray crystallography, is now one of the most powerful tools available to chemists for analyzing the structure of substances.

[See also Hologram and holography; Wave motion ]

Diffraction

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.

Fundamentals

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.

Applications

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.

See also Hologram and holography; Wave motion.

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 The radial scattering of any wave (light, radio, seismic, water, etc.) incident upon an abrupt discontinuity in accordance with Huygens' principle. A fault plane, angular unconformity, small isolated objects (e.g. boulders, fragments of wrecked ships, etc.) will all give rise to the diffraction of incident seismic energy. The quasi-hyperbolic curvature of a seismic diffraction event is related to the velocity within the media through which the diffracted wave travels. In media with slow velocities, the hyperbola is strongly curved, the curvature decreasing as velocity increases.