INTERFERENCE AND DIFFRACTION. The optical phenomena whose discovery established the fact that light is due to wave-motion are those of 'interference' (q.v.) so called. The simplest illus tration of these is due to Thomas Young and is called after him. Three opaque screens are ar ranged in order; in the first there is a narrow slit at 0, illuminated with some homogeneous light. e.g. a flame burning sodium; in the second there are two slits. U, and U. close together parallel to the first and at equal distances from it: the waves spreading out from 0 illuminate the slits U, and so that they in turn become sources of hro identical trains of waves—if the source at flickers or changes in any way, both the second ary sources change together; waves from these two sources illuminate the third screen. Bands parallel to the slits alternately dark and colored, are observed on this screen. These may be ex plained immediately if light is due to wave motion ; because at point,: on the screen such that their distances to 0, and 0, differ by half a wave-length or by an odd number of half wave lengths there will be complete interference. and consequently darkness. Similarly at points on the screen whose distances from the slits 0, and differ by a whole number of wavelengths the two trains of waves will reinforce each other. and there will be light. (lt is evident that there is no destruction of energy—only a redistribution of it.) Referring to the figure. if P is a point in a bri7ht hand fl,P - 0,P = XX. where is any integer number, O. I, 2. 3. etc., and X is the wave length of the waves. If the distance from the receiving screen to the one with the two slits is a; if the distance apart of the two slits is b a -mall quantity compared with a; and if PS is also a small quantity, it is seen by geometry that x O.P—UP a - bx hence N. = a ; and the distance apart of the bright bands is therefore This distance, and both a and b, can be measured; so this experi ment gives a means of determining X. It is found that as the colors ehange from red to yel low to green to blue the wave-length of the corre waves becomes less. It white light is used, the central band at S is white, hut the others arc colored, all merging into each other. The wave-length of the yellow light from a sodium flame is found to be 0.1)0003893 cm.
Since the velocity of the waves is 3x IV ens per second, the NV:1 ve-number for these 'yellow waves' is about 5x 10". This is the number of vibrations per second of the atom of sodium. (For other wave-lengths, see SPECTROSCOPY.) It is thus pos sible now to compare the indices of refraction of a given material—e.g. water—with the corre sponding wave-lengths. A curve plotted with the indices of refraction as ordinates and the wave lengths as abscissa) is called the 'dispersion curve' of the substance. There are many other ways of securing two identical slits as sources of light than the one here described. e.g. Fresnel's bi.prisni and double mirror; but for a full de scription reference should be made to some treatise on light.
(Me of the most interesting phenomena de pending for their explanation upon interference is that of the color of 'thin plates' and of New ton's 'rings,' as shown in the colors of soap-films, very thin films of glass, or when a convex glass lens is pressed closely against a piece of plane glass. When parallel rays of light are incident upon a transparent film of uniform thickness, that portion which comes back, at the proper angle of reflection, is a mixture of waves which have suffered reflection at the top surface of the film and those which, having entered the film, have been reflected at the lower surface and then have emerged directly at the top surface or emerged after a series of internal reflections. If the relative retardation of the component trains of homogeneous waves is such that they have different phases equivalent to a difference of an odd number of half wave-lengths. there will he complete interference: and it can be shown that all the wave, have been transmitted through the film, so there is no loss of energy. If, therefore, the incident light is white, waves will be absent from the reflected beam which satisfy the above condition: and so it will appear colored. It is proved easily that if the thickness of the film is e, its index of refraction with reference to air g, and the angle of incidence of the light or the lower surface of the film a. there will he complete interference in the reflected light for a train of waves whose wavelength in the film is A if NA = 2sacosa.