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famous of the early philosophers, including the great Sir Isaac Newton, to reject the wave theory and to support the projected-particle theory. Within the last hundred years, however, this difficulty has been completely removed, and in addition other properties of light have been discovered for which the wave theory offers the only satisfactory explanation. The most important of these properties will be treated in the next paragraph.
427. Interference of light. Let two pieces of plate glass about half an inch wide and four or five inches long be separated at one end by a thin sheet of paper in the manner shown in Fig. 389, while the other end is clamped or held firmly together, so that a very thin wedge of air exists between the plates. Let a piece of asbestos or blotting paper be soaked in a solution of common salt (sodium chloride) and placed over the tube of a Bunsen burner so as to touch the flame in the manner shown. The flame will be colored a bright yellow by the sodium in the salt. When the eye looks at the reflection of the flame from the glass surfaces, a series of fine black and yellow lines will be seen to cross the plate.
The wave theory offers the following explanation of these effects. Each point of the flame sends out light waves which travel to the glass plate and are in part reflected and in part transmitted at all the surfaces of the glass, that is, at A'B', at AB, at C'D, and at C'D' (Fig. 389). We will consider, however, only those reflections which take place at the two faces of the air wedge, namely, at AB and CD. Let Fig. 390 represent a greatly magnified section of these two surfaces. Let the wavy line as represent a light wave reflected from the surface AB at the point a, and returning thence to the eye.
Interference of light waves
Let the dotted wavy line ir represent a light wave reflected from the surface CD at the point i, and returning thence to the eye. Similarly, let all the continuous wavy lines of the figure represent light waves reflected from different points on AB to the eye, and let all the dotted wavy lines represent waves reflected from corresponding points on CD to the eye. Now, in precisely the same way in which two trains of sound waves from two tuning forks were found, in the experiment illustrating beats (see § 396), to interfere with each other so as to produce silence whenever the two waves corresponded to motions of the air particles in opposite directions, so in this p experiment the two sets of light waves from AB and CD interfere with each other so as to produce darkness wherever these two waves correspond to motions of the light-transmitting medium in opposite directions. The dark bands, then, of our experiment are simply the places at which the two beams reflected from the two surfaces of the air film neutralize or destroy each other, while the light bands correspond to the places at which the two beams reënforce each other and thus produce illumination of double intensity. The position of the second dark band c must of course be determined by the fact that the distance from c to k and back (see Fig. 390) is a wave length more than from a to i and back, and so on down the wedge. This
FIG. 390. Explanation of formation of dark and light bands by interference of light waves
phenomenon of the interference of light is met with in many different forms, and in every case the wave theory furnishes at once a wholly satisfactory explanation of the observed effects, while the corpuscular theory, on the other hand, is unable to account for any of these interference effects without the most fantastic and violent assumptions. Hence the corpuscular theory is now practically abandoned, and light is universally regarded by physicists as a form of wave motion.
428. The ether. We have already indicated that if the wave theory is to be accepted, we must conceive, with Huygens, that all space is filled with a medium, called the ether, in which the waves can travel. This medium cannot be like any of the ordinary forms of matter; for if any of these forms existed in interplanetary space, the planets and the other heavenly bodies would certainly be retarded in their motions. As a matter of fact, in all the hundreds of years during which astronomers have been making accurate observations of the motions of heavenly bodies no such retardation has ever been observed. The medium which transmits light waves must therefore have a density which is infinitely small even in comparison with that of our lightest gases.
Further, in order to account for the transmission of light through transparent bodies, it is necessary to assume that the ether penetrates not only all interstellar spaces but all intermolecular spaces as well.
429. Wave length of yellow light. Although light, like sound, is a form of wave motion, light waves differ from sound waves in several important respects. In the first place, an analysis of the preceding experiment, which seems to establish so conclusively the correctness of the wave theory, shows that the wave length of light is extremely minute in comparison with that of ordinary sound waves. The wave length of the yellow light used in that experiment is .00006 centimeter (about 40,000 inch).
The number of vibrations per second made by the little particles which send out the light waves may be found, as in the case of sound, by
dividing the velocity by the wave length. Since the velocity of light is 30,000,000,000 centimeters per second and the wave length is .00006 centimeter, the number of vibrations per second of the particles which emit yellow light has the enormous value 500,000,000,000,000.
430. Wave theory explanation of refraction. Let one look vertically down upon a glass or tall jar full of water and place his finger on the side of the glass at the point at which the bottom appears to be, as seen through the water (Fig. 391). In every case it will be found that the point touched by the finger will be about one fourth of the depth of the water above the bottom..
According to the wave theory this effect is due to the fact that the speed of light is less in water than in air. Thus, consider a wave which originates at any point P (Fig. 392) beneath a surface of water and spreads from that point with equal speed in all directions. At the instant at which the front of this wave first touches the surface at o it will, of course, be of spherical form, having P as its center. Let aob be a section of this sphere. An instant later, if the speed had not changed in. passing into air, the wave would have still had P as its center, and its form would have coincided with the dotted line cod, so drawn that ac, oo,, and bd are all equal. But if the velocity in air is greater than in water, then at the instant considered the disturbance will have reached some point o instead of 019 and hence the emerging wave will actually have the form of the heavy line cod instead of the dotted line cod. Now this wave cod is more curved than the old wave aob, and hence it has its center at some point P' above P. In other words, the wave has bulged upward in passing from water into air. Therefore, when a section of this wave enters the eye at E, the wave appears to originate not at P but at P', for the light actually comes to the eye from P' as a center
FIG. 391. Apparent elevation of the bottom of a body of water
rather than from P. We conclude, therefore, that if light travels more slowly in water than in air, all objects beneath the surface of water ought to appear nearer to the eye than they actually are. This is precisely what we found to be the case in our experiment.
Furthermore, since when the eye is in any position other than E, for example E', the light travels to it over the broken path PdE', the construction shows that light is always bent away from the perpendicular when it passes obliquely into a medium in which the speed is greater. If it had passed into a medium of less speed, the point P would have appeared depressed below its natural position, because the wave, on emerging into the slower medium, instead of bulging upward would be flattened, and therefore would have its center of curvature, or apparent point of origin, below P; hence the oblique rays would have appeared to be bent toward the perpendicular, as we found in § 423 to be the case.
431. The ratio of the speeds of light in air and water. The experiment with the tall jar of water in § 430 not only indicates qualitatively that the speed of light in air is greater than in water, but it furnishes a simple means of determining the ratio of the two speeds. Thus, in Fig. 392 the line oo, represents just how far the wave travels in air while it is
traveling the distance ac (=00,) in water. Hence ratio of the speeds of light in air and in water.
FIG. 392. Representing a wave emerging from water into air