The Wave Theory of Light.
There have been several theories about the nature of light. The great English physicist, Isaac Newton (1642-1727), who was a pioneer in the study of light as well as in that of mechanics, favoured an atomic explanation of light; i.e., he thought that it consisted of particles or light corpuscules which were emitted from luminous bodies like projectiles from a cannon. In contrast to this “emission” theory was the wave theory of Newton’s contemporary, the Dutch scientist, Huygens. According to him, light was a wave motion passing from luminous bodies into a substance called the ether, which filled the otherwise empty universe and permeated all bodies, at least all transparent ones. In the nineteenth century the wave theory, particularly through the work of the Englishman, Young, and the Frenchman, Fresnel, came to prevail over the emission theory. Since the wave theory plays an important part in the following chapters, a discussion of the general characteristics of all wave motions is appropriate here. The examples will include water waves on the surface of a body of water, and sound waves in air.
Fig. 4.—Photograph of the interference between two similar wave systems.
Fig. 5.—A section of the same picture enlarged.
(From Grimsehl, Lehrbuch der Physik.)
Let us suppose that we are in a boat which is anchored on a body of water and let us watch the regular waves which pass us. If there is neither wind nor current, a light body like a cork, lying on the surface, rises with the wave crests and sinks with the troughs, going forward slightly with the former and backward with the latter, but remaining, on the whole, in the same spot. Since the cork follows the surrounding water particles, it shows their movements, and we thus see that the individual particles are in oscillation, or more accurately, in circulation, one circulation being completed during the time in which the wave motion advances a wave-length, i.e., the distance from one crest to the next. This interval of time is called the time of oscillation, or the period. If the number of crests passed in a given time is counted, the oscillations of the individual particles in the same time can be determined. The number of oscillations in the unit of time, which we here may take to be one minute, is called the frequency. If the frequency is forty and the wave-length is three metres, the wave progresses 3 × 40 = 120 metres in one minute. The velocity with which the wave motion advances, or in other words its velocity of propagation, is then 120 metres per minute. We thus have the rule that velocity of propagation is equal to the product of frequency and wave-length ([cf. Fig. 8]).
On the surface of a body of water there may exist at the same time several wave systems; large waves created by winds which have themselves perhaps died down, small ripples produced by breezes and running over the larger waves, and waves from ships, etc. The form of the surface and the changes of form may thus be very complicated; but the problem is simplified by combining the motions of the individual wave systems at any given point. If one system at a given time gives a crest and another at the same instant also gives a crest at the same point, the two together produce a higher crest. Similarly, the resultant of two simultaneous troughs is a deeper trough; a crest from one system and a simultaneous trough from the other partially destroy or neutralize each other. A very interesting yet simple case of such “interference” of two wave systems is obtained when the systems have equal wave-lengths and equal amplitudes. Such an interference can be produced by throwing two stones, as much alike as possible, into the water at the same time, at a short distance from each other. When the two sets of wave rings meet there is created a network of crests and troughs. Figs. 4 and 5 show photographs of such an interference, produced by setting in oscillation two spheres which were suspended over a body of water.
Fig. 6.—Schematic representation of an interference.
In [Fig. 6] there is a schematic representation of an interference of the same nature. Let us examine the situation at points along the lower boundary line. At 0, which is equidistant from the two wave centres, there is evidently a wave crest in each system; therefore there is a resultant crest of double the amplitude of a single crest if the two systems have the same amplitude. Half a period later there is a trough in each system with a resultant trough of twice the amplitude of a single trough. Thus higher crests and deeper troughs alternate. The same situation is found at point 2, a wave-length farther from the left than from the right wave centre; in fact, these results are found at all points such as 2, 2′, 4 and 4′, where the difference in distance from the two wave centres is an even number of wave-lengths. At the point 1, on the other hand, where the difference between the distance from the centres is one-half a wave-length, a crest from one system meets a trough from the other, and the resultant is neither crest nor trough but zero. There is the same result at points 1′, 3, 3′, 5, 5′, etc., where the difference between the distances from the two wave centres is an odd number of half wave-lengths. By throwing a stone into the water in front of a smooth wall an interference is obtained, similar to the one described above. The waves are reflected from the wall as if they came from a centre at a point behind the wall and symmetrically placed with respect to the point where the stone actually falls.
Fig. 7.—Waves which are reflected by a board and pass through a hole in it.
When a wave system meets a wall in which there is a small hole, this opening acts as a new wave centre, from which, on the other side of the wall, there spread half-rings of crests and troughs. But if the waves are small and the opening is large in proportion to the wave-length, the case is essentially different. Let us suppose that wave rings originate at every point of the opening. As a result of the co-operation of all these wave systems the crests and troughs will advance, just as before, in the original direction of propagation, i.e., along straight lines drawn from the original wave centre through the opening; lines of radiation, we may call them. It can be shown, however, that as these lines of radiation deviate more and more from the normal to the wall, the interference between wave systems weakens the resultant wave motion. If the deviation from the normal to the wall is increased, the weakening varies in magnitude, provided that the waves are sufficiently small; but even if the wave motions at times may thus “flare up” somewhat, still on the whole they will decrease as the deviation from the normal to the wall is increased. The smaller the waves in comparison to the opening, the more marked is the decrease of the wave motions as the distance from the normal to the wall is increased, and the more nearly the waves will move on in straight lines. That light moves in straight lines, so that opaque objects cast sharp shadows, is therefore consistent with the wave theory, provided the light waves are very small; though it is reasonable to expect that on the passage of light through narrow openings there will be produced an appreciable bending in the direction of the rays. This supposition agrees entirely with experiment. As early as the middle of the seventeenth century, the Italian Grimaldi discovered such a diffraction of light which passes through a narrow opening into a dark room.
Fig. 8.—Schematic representation of a wave.
A and B denote crests; C denotes a trough.
λ = wave-length. α = amplitude of wave.
If T denotes the time the wave takes to travel
from A to B, and ν = 1/T the frequency, the
wave velocity v will be equal to λ/T = λν.
Points P and P′ are points in the same phase.
In both light and sound the use of such terms as wave and wave motion is figurative, for crests and troughs are lacking. But this choice of terms is commendable, because sound and light possess an essential property similar to one possessed by water waves. What happens when a tuning-fork emits sound waves into the surrounding air, is that the air particles are set in oscillation in the direction of the propagation of sound. All the particles of air have the same period as the tuning-fork, and the number of oscillations per second determines the pitch of the note produced; but the air particles at different distances from the tuning-fork are not all simultaneously in the same phase or condition of oscillation. If one particle, at a certain distance from the source of sound and at a given time, is moving most rapidly away from the source, then at the same time there is another particle, somewhat farther along the direction of propagation, which is moving towards the source most rapidly. This alternation of direction will exist all along the path of the sound. Where the particles are approaching each other, the air is in a state of condensation, and where the particles are drawing apart, the air is in a state of rarefaction. While the individual particles are oscillating in approximately the same place, the condensations and rarefactions, like troughs and crests in water, advance with a velocity which is called the velocity of sound. If we call the distance between two consecutive points in the same phase a wave-length, and the number of oscillations in a period of time the frequency, then, as in the case of water waves, the velocity of propagation will be equal to the product of frequency and wave-length.
Light, like sound, is a periodic change of the conditions in the different points of space. These changes which emanate from the source of light, in the course of one period advance one wave-length, i.e., the distance between two successive points in the same phase and lying in the direction of propagation. As in the cases of sound and water waves, the velocity of propagation or the velocity of light is equal to the product of frequency and wave-length. If this velocity is indicated by the letter c, the frequency by ν and the wave-length by λ, then
| c = νλ or ν = | c | or λ = | c |
| λ | ν |
The velocity of light in free space is a constant, the same for all wave-lengths. It was first determined by the Danish astronomer Ole Rømer (1676) by observations of the moons of Jupiter. According to the measurements of the present day the velocity of light is about 1,000,000,000 feet or 300,000 kilometres per second. In centimetres it is thus about 3 × 10¹⁰.
Efforts have been made to consider light waves, like sound waves, as produced by the oscillations of particles, not of the air, but of a particular substance, the “ether,” filling and permeating everything; but all attempts to form definite representations of the material properties of the ether and of the movements of its particles have been unsuccessful. The electromagnetic theory of light, enunciated about fifty years ago by the Scottish physicist, Maxwell, has furnished information of an essentially different character concerning the nature of light waves.
Let us suppose that electricity is oscillating in a conductor connecting two metal spheres, for instance. The spheres, therefore, have, alternately, positive and negative charges. Then according to Maxwell’s theory we shall expect that in the surrounding space there will spread a kind of electromagnetic wave with a velocity equal to that of light. Wherever these waves are, there should arise electric and magnetic forces at right angles to each other and to the direction of propagation of the waves; the forces should change direction in rhythm with the movements of electricity in the emitting conductor. By way of illustration let us assume that we have somewhere in space an immensely small and light body or particle with an electric charge. If, in the region in question, an electromagnetic wave motion takes place, then the charged particle will oscillate as a result of the periodically changing electrical forces. The particle here plays the same rôle as the cork on the surface of the water ([cf. p. 35]); the charged body thus makes the electrical oscillations in space apparent just as the cork shows the oscillations of the water. In addition to the electrical forces there are also magnetic forces in an electromagnetic wave. We can imagine that they are made apparent by using a very small steel magnet instead of the charged body. According to Maxwell’s theory, the magnet exposed to the electromagnetic wave will perform rapid oscillations. Maxwell came to the conclusion that light consisted of electromagnetic waves of a similar nature, but much more delicate than could possibly be produced and made visible directly by electrical means.
In the latter part of the nineteenth century the German physicist, H. Hertz, succeeded in producing electromagnetic waves with oscillations of the order of magnitude of 100,000,000 per second, corresponding to wave-lengths of the order of magnitude of several metres.
| ( λ = | c | = | 3 × 10¹⁰ | = 300 cm. ) |
| ν | 10⁸ |
Moreover, he proved the existence of the oscillating electric forces by producing electric sparks in a circle of wire held in the path of the waves. He showed also that these electromagnetic waves were reflected and interfered with each other according to the same laws as in the case of light waves. After these discoveries there could be no reasonable doubt that light waves were actually electromagnetic waves, but so small that it would be totally impossible to examine the oscillations directly with the assistance of electric instruments.
But there was in this work of Hertz no solution of the problems about the nature of ether and the processes underlying the oscillations. More and more, scientists have been inclined to rest satisfied with the electromagnetic description of light waves and to give up speculation on the nature of the ether. Indeed, within the last few years, specially through the influence of Einstein’s theory of relativity, many doubts have arisen as to the actual existence of the ether. The disagreement about its existence is, however, more a matter of definition than of reality. We can still talk about light as consisting of ether waves if we abandon the old conception of the ether as a rigid elastic body with definite material properties, such as specific gravity, hardness and elasticity.