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interference, in physics, the effect produced by the combination or superposition of two systems of waves, in which these waves reinforce, neutralize, or in other ways interfere with each other. Interference is observed in both sound waves and electromagnetic waves, especially those of visible light and radio.
Interference in Sound Waves
When two sound waves occur at the same time and are in the same phase, i.e., when the condensations of the two coincide and hence their rarefactions also, the waves reinforce each other and the sound becomes louder. This is known as constructive interference. On the other hand, two sound waves occurring simultaneously and having the same intensity neutralize each other if the rarefactions of the one coincide with the condensations of the other, i.e., if they are of opposite phase. This canceling is known as destructive interference. In this case, the result is silence.
Alternate reinforcement and neutralization (or weakening) take place when two sound waves differing slightly in frequency are superimposed. The audible result is a series of pulsations or, as these pulsations are called commonly, beats, caused by the alternate coincidence of first a condensation of the one wave with a condensation of the other and then a condensation with a rarefaction. The beat frequency is equal to the difference between the frequencies of the interfering sound waves.
Interference in Light Waves
Light waves reinforce or neutralize each other in very much the same way as sound waves. If, for example, two light waves each of one color (monochromatic waves), of the same amplitude, and of the same frequency are combined, the interference they exhibit is characterized by so-called fringes—a series of light bands (resulting from reinforcement) alternating with dark bands (caused by neutralization). Such a pattern is formed either by light passing through two narrow slits and being diffracted (see diffraction), or by light passing through a single slit. In the case of two slits, each slit acts as a light source, producing two sets of waves that may combine or cancel depending upon their phase relationship. In the case of a single slit, each point within the slit acts as a light source. In all cases, for light waves to demonstrate such behavior, they must emanate from the same source; light from distinct sources has too many random differences to permit interference patterns.
The relative positions of light and dark lines depend upon the wavelength of the light, among other factors. Thus, if white light, which is made up of all colors, is used instead of monochromatic light, bands of color are formed because each color, or wavelength, is reinforced at a different position. This fact is utilized in the diffraction grating, which forms a spectrum by diffraction and interference of a beam of light incident on it. Newton's rings also are the result of the interference of light. They are formed concentrically around the point of contact between a glass plate and a slightly convex lens set upon it or between two lenses pressed together; they consist of bright rings separated by dark ones when monochromatic light is used, or of alternate spectrum-colored and black rings when white light is used. Various natural phenomena are the result of interference, e.g., the colors appearing in soap bubbles and the iridescence of mother-of-pearl and other substances.
Interference as a Scientific Tool
The experiments of Thomas Young first illustrated interference and definitely pointed the way to a wave theory of light. A. J. Fresnel's experiments clearly demonstrated that the interference phenomena could be explained adequately only upon the basis of a wave theory. The thickness of a very thin film such as the soap-bubble wall can be measured by an instrument called the interferometer. When the wavelength of the light is known, the interferometer indicates the thickness of the film by the interference patterns it forms. The reverse process, i.e., the measurement of the length of an unknown light wave, can also be carried out by the interferometer.
The Michelson interferometer used in the Michelson-Morley experiment of 1887 to determine the velocity of light had a half-silvered mirror to split an incident beam of light into two parts at right angles to one another. The two halves of the beam were then reflected off mirrors and rejoined. Any difference in the speed of light along the paths could be detected by the interference pattern. The failure of the experiment to detect any such difference threw doubt on the existence of the ether and thus paved the way for the special theory of relativity.
Another type of interferometer devised by Michelson has been applied in measuring the diameters of certain stars. The radio interferometer consists of two or more radio telescopes separated by fairly large distances (necessary because radio waves are much longer than light waves) and is used to pinpoint and study various celestial sources of radiation in the radio range. Astronomical interferometers consisting of two or more optical telescopes are used to enhance visible images of distant celestial objects. See radio astronomy; virtual telescope.
The interference pattern of fringes formed at a particular position is the sum of the intensities of the two interacting waves at that position. The fringes occur because of differences in pathlength between interacting waves, i.e. because of unequal distances from source to interaction point. If the difference is a whole number of wavelengths, then wave peaks (or troughs) of the two interacting waves coincide and the waves reinforce one another, producing a bright fringe when light waves are involved; this is termed constructive interference. If the path difference is an integral number of half wavelengths a peak coincides with a wave trough and a dark fringe results; this is destructive interference.
Both constructive and destructive interference of light can be produced by means of thin films of uniform thickness, as used in interference filters. Waves of selected wavelengths are reflected from the front and back surfaces of the film and by a suitable choice of film composition and thickness the waves will either be reinforced or will cancel each other.
See also interferometer.
(1) In biology, the influence of the crossover of homologous chromosomes in one area on the appearance of new crossovers in neighboring areas. Most often this type of interference inhibits the appearance of a new crossover in a neighboring area; hence, in experiments the percentage of double-crossover individuals as a rule turns out to be lower than that theoretically expected. Double crossover is particularly strongly suppressed by interference when there are small distances between the genes.
(2) In medicine, interference of viruses is the suppression by one virus of the effect of another when there is a mixed infection.In such cases the first virus is called the interfering one, and the second is called the pretender.
(of waves), superposition of two or more waves in space, producing an increase or decrease in the amplitude of the resulting wave. Interference is characteristic of all waves, regardless of their nature: waves on the surface of a liquid, elastic waves (such as sound waves), and electromagnetic waves (such as radio or light waves).
If two waves are propagating through space, then the resulting oscillation at every point is the geometric sum of the oscillations corresponding to each of the component waves. This “superposition principle” is usually strictly obeyed and is violated only in the propagation of waves in a medium if the amplitude (intensity) of the waves is very large. Wave interference is possible if the waves are coherent.
The simplest case of interference is the addition of two waves of identical frequency and phase. In this case, if the oscillations take place according to a sine (harmonic) law, the amplitude of the resultant wave at any point in space is
where A1 and A2 are the amplitudes of the component waves and ϕ is the phase difference between the waves at the point in question. If the waves are coherent, the phase difference ϕ remains unchanged at the given point but may change from point to point, leading to a distribution of the amplitudes of the resultant waves with alternating maximums and minimums. If the amplitudes of the component waves are the same (that is, if A1A2), the maximum amplitude is equal to twice the amplitude of each wave, and the minimum amplitude is equal to zero. The geometric loci of equal phase difference, which specifically corresponds to the maximums or minimums, are surfaces that depend on the properties and location of the sources emitting the component waves. In the case of two point sources emitting spherical waves, the surfaces are hyperboloids of rotation.
Another important instance of interference is the superposition of two plane waves propagating in opposite directions (for example, incident and reflected waves). In this case standing waves are produced.
The average values of the energy flux of the wave over the period is proportional to the square of the amplitude. Therefore, it follows from the equation for the resultant amplitude that interference involves a redistribution of the energy flux of the wave in space. The distribution of amplitudes with alternating minimums and maximums, which is characteristic of interference, remains stationary in space or moves so slowly that the maximums and minimums are not displaced by a quantity comparable to the distance between them during the time required for the observation, and it may be observed only when the waves are coherent. If the waves are incoherent, then the phase difference ϕ changes rapidly and at random, assuming all possible values, so that the average value of cos ϕ is zero. In this case, the average value of the amplitude of the resultant wave is found to be the same at different points, the maximums and minimums are blurred, and the interference pattern disappears. In this case, the mean square of the resultant amplitude is equal to the sum of the mean squares of the amplitudes of the component waves—that is, superposition of waves involves the addition of the energy fluxes or intensities.
The main features of the interference phenomenon described above apply equally to elastic and electromagnetic waves. However, although coherence of sonic and radio waves is easily achieved (for example, by using the same current to feed various antennas or speakers), before the development of the laser coherent light beams could be produced only by the same light source, using special methods. Another essential difference between the methods of interference production involving sonic and radio waves on the one hand and light waves on the other is related to the size of the emitters. The size of the sonic and radio-wave emitters is almost always comparable with the length of the emitted wave, whereas in the case of light waves, the size of the source is almost always large in comparison with the wavelength. For this reason, the problem of the extent of the source plays a significant role in the interference of light waves. Because of these special features, light interference may be observed only under special conditions.
Wave interference is of great importance in both research and technology. Since a definite relationship exists among the wavelength, the path difference of interfering rays, and the position of maximums and minimums, knowledge of the path difference of the interfering waves makes possible determination of the wavelength from the positions of the minimums and maximums and, conversely, knowledge of the wavelength makes possible determination of the path difference of the rays (that is, measurement of distances) from the positions of the maximums and minimums. Instruments using wave interference include optical interferometers, radio interferometers, and interferential radio range finders.
REFERENCESElementarnyi uchebnik fiziki, 6th ed., vol. 3, ch. 3. Edited by G. S. Landsberg. Moscow, 1970.
Gorelik, G. S. Kolebaniia i volny, 2nd ed. Moscow-Leningrad, 1959.
Landsberg, G. S. Optika, 4th ed. Moscow, 1957. (Obshchii kurs fiziki, vol. 3.)