Interference

Type of physical science: Classical physics

Field of study: Optics

When two light beams are superimposed under appropriate conditions, alternate regions of brightness and darkness appear. If white light is used, the bright regions are colored. This interference of light is a commonly observed phenomenon and finds application in a wide variety of fields.

Overview

The phenomenon of interference can be illustrated by a double-slit experiment, which was first performed in 1802 by Thomas Young. When the light emitted by two sources, such as two electric bulbs, overlaps in a region, this region is more brightly illuminated then the nonoverlapping areas. On the other hand, consider the light from a monochromatic source, which emits light of same color or wavelength, passing through two narrow vertical slits cut into an opaque screen and falling into a viewing screen. (The combined length of a wave crest and a trough of a wave is called its wavelength.) The two narrow vertical slits are separated by a small distance and directly opposite to the source. The result of passing light through these two slits is quite different from that of the first experiment. Alternately bright and dark bands appear parallel to the length of the slits. These bands are known as fringes, and the phenomenon giving rise to these fringes is called interference.

The interference phenomenon is easy to understand if light is considered to be in the form of waves. According to classical theory, light travels in the form of waves, such as water waves. These waves are made of crests (rising part) and troughs (falling part). For some locations of the screen, the arrival of a wave crest (or trough) from one source always coincides with the arrival of a crest (or trough) from the other source. Such a location is called a region of constructive interference, or interference maximum. If the two light sources are of the same intensity or brightness, the resultant wave in the interference maximum region has twice the amplitude as that of a single wave. (The amplitude in this case refers to the height of the crest or the depth of the trough.) At some other location, the arrival of a crest from one source always coincides with the arrival of a trough from the other. If they are of the same amplitude, they cancel each other and a region of destructive interference, or interference minimum, exists. The two sources--that is, the two illuminated slits--maintain the same constant relative phase; that is, they are always in step because they are both from the same parent source. Hence, the waves keep producing the constructive and destructive interferences in the same regions, and a stationary interference pattern is observed. It should be noted that in this superposition of light waves, the light wave from each source acts independently, as though the other source were not there, which creates the resultant effect.

In the double-slit experiment, the interference fringes are parallel. To obtain well-defined fringes, the two slits must be narrow and separated by a very small distance. In this experiment, consider two corresponding points in the two illuminated slits. For any point on the screen (except the midpoint), the light travels in different paths; the path difference controls mainly the nature of interference, that is, whether it is constructive or destructive. When the path difference is zero or an integral multiple of the wavelength of the source, there will be constructive interference. If the path difference is an odd multiple of half the wavelength, there will be destructive interference.

Suppose the monochromatic source is replaced with a white light source, such as a carbon arc lamp or a frosted electric bulb (known as a composite source because it contains all colors from violet to red). The different colors have different wavelengths; therefore, in the regions of constructive interference, different colors produce interference maxima at different places. Thus, all bright bands appear as colored bands, except the central bright band, which will remain white, since all the colors overlap.

One may wonder why the light from two electric bulbs does not produce interference as in the double-slit experiment. In the basic mechanism of emission of light, excited atoms in the light source radiate energy as electromagnetic radiation. Each excited atom radiates energy for about a millionth of a second and ceases when it returns to its ground or unexcited state.

Meanwhile, other atoms have begun to radiate. The phases of these emitted radiations are random; if there are two such sources, such as the electric bulbs, there will be no definite phase relationship between the two radiations. In other words, they will not be in step. Hence, when they interfere at a location, that region can be alternately bright and dark in rapid succession and only uniform illumination can be seen. Two monochromatic sources that have a constant phase relationship are said to be coherent. Besides these conditions for coherence, there are a few other conditions to be satisfied to obtain well-defined interference fringes. The source preferably should be a point source or a line source, such as the narrow illuminated slit. If the source has a finite width, the angle subtended by it at the double-slit or other interference system should be very small compared to the ratio of the wavelength of the light to the distance between the interference sources.

There are many ways of producing coherent sources similar to Young's experiments with slits. Many successful interference experiments have been performed using a source and its image from a mirror, biprisms, bimirrors, split lenses, and the like. These are generally known as interference by division of wavefront. As light from a source travels through a medium, the different particles of the medium are set into vibration. The locus of all points that are in the same state of vibration is called a wavefront. In geometrical optics, where light is studied on the basis of some geometrical laws, light is considered to be traveling in the form of rays and beams.

In physical optics, where scientists are interested in the physical nature of light, light can be thought of as traveling in the form of wavefronts. A point source sends out a spherical wavefront in a homogeneous transparent medium, and an illuminated slit sends out a cylindrical wavefront.

Both of these wavefronts at a very large distance from the source become plane wavefronts.

Another major class of interference is by division of amplitude. In this case, light from an extended source is partially reflected in successive layers of transparent plates or films, and the reflected portions of the original beam can overlap and produce interference. These reflected portions give rise to very interesting interference patterns, such as the concentric circular fringes called Newton's rings, or the beautiful colored patterns seen on soap bubbles or thin oil films reflecting sunlight. In the latter case, the condition of maximum and minimum for the different colors in the sunlight change with the thickness of the film or the angle at which the films are viewed. That explains why the soap bubble or oil film keeps changing color as it becomes thinner as a result of evaporation or spreading or as it is viewed at different angles.

Applications

A simple knowledge of the interference phenomenon helps scientists understand the brilliant colors seen when sunlight falls on a layer of oil spreading on a wet road or even when one sees the colorful throat of a hummingbird. In both cases, certain wavelengths in the light striking the oil film or hummingbird feathers undergo destructive interference. The brilliant remainder is seen as reflection.

The interference effect has found a wide variety of applications, such as measuring the thickness of thin films, refractive index of exotic liquids, and angular diameter of stars, or even to make antireflection coatings on camera lenses. An instrument using the principle of interference for some of these applications is generally known as an interferometer.

One condition for fringes to be produced by Young's slit experiment was a restriction on the angular size of the source as seen from the slits. This restriction suggests that such a system can be used to measure the angular size of the source by altering the slit separation until fringes could not be seen. Albert A. Michelson applied this principle to construct his stellar interferometer. In the early 1920's, Michelson set up his interferometer on the 254-centimeter Hooker telescope at Mount Wilson Observatory in California and measured the angular diameter of the star Betelgeuse in the constellation Orion. His measurement showed that this star is about three hundred times that of the sun; it is known as a red giant.

The interference by division of amplitude involved the reflection of light by the two surfaces of thin films. Michelson used the air film formed between two front-face mirrors to obtain interference fringes. If one of the mirrors is moved slowly on machine tracks parallel to itself, the fringes moved laterally in the line of sight. By counting the number of fringes, the distance moved by the mirror can be calculated with an accuracy on the order of a millionth of a millimeter. Michelson used this interferometer to standardize the measuring length--meter--in terms of the wavelength of a cadmium source.

If a thin film of transparent material is introduced in the path of the light from one of the interfering sources, the whole fringe system is shifted through a distance that depends on the thickness of the film and its refractive index. Hence, by measuring the shift in the fringe system, the thickness, or refractive index, of the film can be measured accurately.

The Fabry-Perot interferometer, first constructed in 1899, uses the principle of multiple-beam interference to produce sharply defined, very narrow, concentric, and circular fringes. If the source is not monochromatic and has two very close wavelengths, the interferometer will then produce two ring systems that can be seen as separate. This instrument is very useful in the study of the hyperfine structure of spectral lines; that is, very closely packed spectral lines can be resolved and studied. As spectral lines are of atomic origin, such studies are important for the understanding of atomic structure.

Interference fringes also can be used to test the flatness of a glass surface. The plate to be tested is placed on a perfectly flat glass plate to form a wedge-shaped air film in between.

When the plates are illuminated from above by a monochromatic light, alternatively bright and dark parallel fringes are seen parallel to the line of contact of the two plates. If the plate to be tested is not perfectly flat, these fringes will not be quite straight.

In optical instruments using lenses and prisms, such as binoculars, telescopes, and cameras, there is considerable loss of intensity because of partial reflection at the glass-air interface. At each interface, 4 to 6 percent of the incident light may be lost. Because of this, the final image not only is dim but also suffers from the background haze created by the reflected light, which may be scattered into the field of view. Hence, it is now common practice to coat an optical component, such as the camera lens, with an antireflection coating, which actually uses the principle of destructive interference. If a surface is coated with a thin film of thickness equal to one-fourth of the wavelength of the incident light or multiples thereof, the partially reflected lights from its top and bottom surfaces will almost cancel each other because of destructive interference. A single quarter-wavelength layer of magnesium fluoride will reduce the reflection of glass from 4 percent to 1 percent over the visible spectrum. Double-layer coatings using magnesium fluoride and zinc sulfide can be even more effective and are widely used as antireflection coatings.

Perhaps the most exciting application of interference is the hologram, a two-dimensional photographic plate that provides a faithful reproduction of a scene in three dimensions. A conventional photograph is a recording of an image, whereas a hologram is a recording of the interference pattern resulting from the combination of two sets of wavefronts.

One set of wavefronts is from light reflected by the object, and the other set of wavefronts is from the reference beam that is diverted from the coherent source (a laser) directly to the photographic plate. An ordinary photograph records only the amplitude of the light from the object photographed. A hologram records both the amplitude and the phase of the light from the object. The hologram is actually a photograph of microscopic interference fringes. When it is viewed through a coherent beam of light from a laser, the light going through these microscopic interference fringes produces wavefronts identical in form to the original wavefronts reflected by the object.

Context

The evolution of an understanding of the physical nature of light forms one of the most fascinating accounts in the history of science. In the seveneteenth century, Sir Isaac Newton and Christiaan Huygens pioneered two different theories for the nature of light. According to Newton, light is of particle nature, whereas Huygens viewed light to be in the form of waves.

This controversy raged for nearly three centuries until the advent of quantum electrodynamics, which reconciled the wave-particle duality of light. The interference phenomenon can be explained only on the basis of wave theory. Young's double-slit interference experiment performed in 1802, and its successful application to determine the wavelength of the monochromatic source, strongly supported the wave theory and led to its development. Thus, Young's experiment is one of the most historically significant experiments. The wave theory was developed further by James Clerk Maxwell, who showed that light is in the form of electromagnetic waves. These waves are made up of an electric component and a magnetic component; these components are locked in step at right angles to each other and fluctuate together.

The interference studies have increased the understanding and appreciation of nature.

When one sees the brilliant colors of a soap bubble in sunlight or the beautiful iridescence in mother-of-pearl, peacock feathers, and butterfly wings, the initial admiration often leads to the question of their origin. Their interpretation in terms of interference in thin films is simple and elegant.

The understanding of a phenomenon always leads to important applications. A single instrument such as Michelson's interferometer has been used in a variety of ways, such as to establish experimental evidence for the validity of the theory of special relativity, to detect and measure hyperfine structure in line spectra, to measure the tidal effect of the Moon on Earth, and to provide a substitute standard for the meter in terms of wavelength of light.

As new discoveries are made, the interference phenomenon will play a more significant role. For example, the basic principle of holography through wavefront reconstruction was suggested by Dennis Gabor in 1948, but it became useful and popular only after the invention of the laser in the 1960's. Holography, which uses the basic principle of interference, finds application in many fields, such as art, advertising, optics, and engineering.

Principal terms

AMPLITUDE: the extent of vibration on either side of the equilibrium position; in wave motion, the height of a crest or the depth of a trough gives the amplitude

COHERENT LIGHT: light whose waves are all in step; for two light sources to be coherent, they should be monochromatic and have a constant phase relationship

FRINGES: alternately bright and dark or color bands

HYPERFINE STRUCTURE: a presumably single spectral line showing a structure of more components under very close observation

INTENSITY: the brightness of light, which is directly proportional to the square of the amplitude

MONOCHROMATIC SOURCE: a light source of single wavelength

WAVEFRONT: the locus of all points that are in the same state of vibration

WAVELENGTH: the length of a wave crest and trough together

Bibliography

Graham-Smith, Francis, and J. H. Thomson. OPTICS. London: John Wiley, 1971. Contains some mathematical equations, but the description and figures are clear enough for the average reader. Good presentation of topic.

Hecht, Eugene. OPTICS. 2d ed. Reading, Mass.: Addison-Wesley, 1987. Contains both descriptive and mathematical material. The mathematical discussions, however, can be omitted by those who find it difficult. The descriptive portions of chapters 7 and 9 give an excellent account of interference and wave motion.

Hewitt, Paul G. CONCEPTUAL PHYSICS. 6th ed. Glenview, Ill.: Scott, Foresman, 1989. The wave nature of light, light emission, and the interference phenomeon are described in nontechnical language. Includes examples from day-to-day life in chapter 28. An introductory text for nonscience majors.

Jenkins, Francis A., and Harvey E. White. FUNDAMENTALS OF OPTICS. 4th ed. New York: McGraw-Hill, 1976. Follows a traditional approach. Chapters 12 to 14 discuss interference and its applications, with necessary background material. A classic text.

Kittel, Charles, et al. WAVES. Berkeley Physics Course Vol. 3. New York: McGraw-Hill, 1965-1971. Although a bit technical, the thoughtful presentation makes it worth reading even for the general reader.

Pedrotti, Frank L., and Leno S. Pedrotti. INTRODUCTION TO OPTICS. Englewood Cliffs, N.J.: Prentice-Hall, 1987. Well-written and modern textbook. Chapters 1 and 13 to 15 are applicable. The technical material can be overlooked without hurting the descriptive parts.

Van Heel, A. C. S., and C. H. F. Velzel. WHAT IS LIGHT? New York: McGraw-Hill, 1968. Chapters 1 and 3 discuss interference and the background needed for its understanding. Contains minimal mathematics. Excellent figures and photographs.

Young's double-slit experiment displayed the wave nature of light