Objections to the Undulatory Theory, from a difference in the Action of Sound and Light under the same circumstances, removed—The Dispersion of Light according to the Undulatory Theory—Arago’s final proof that the Undulatory Theory is the Law of Nature.

The numerous phenomena of periodical colours arising from the interference of light, which do not admit of satisfactory explanation on any other principle than the undulatory theory, are the strongest arguments in favour of that hypothesis; and even cases which at one time seemed unfavourable to that doctrine have proved upon investigation to proceed from it alone. Such is the erroneous objection which has been made, in consequence of a difference in the mode of action of light and sound, under the same circumstances, in one particular instance. When a ray of light from a luminous point, and a diverging sound, are both transmitted through a very small hole into a dark room, the light goes straight forward and illuminates a small spot on the opposite wall, leaving the rest in darkness; whereas the sound on entering diverges in all directions, and is heard in every part of the room. These phenomena, however, instead of being at variance with the undulatory theory, are direct consequences of it, arising from the very great difference between the magnitude of the undulations of sound and those of light. The undulations of light are incomparably less than the minute aperture, while those of sound are much greater. Therefore when light, diverging from a luminous point, enters the hole, the rays round its edges are oblique, and consequently of different lengths, while those in the centre are direct, and nearly or altogether of the same lengths. So that the small undulations between the centre and the edges are in different phases, that is, in different states of undulation. Therefore the greater number of them interfere, and by destroying one another produce darkness all around the edges of the aperture; whereas the central rays, having the same phases, combine, and produce a spot of bright light on a wall or screen directly opposite the hole. The waves of air producing sound, on the contrary, being very large compared with the hole, do not sensibly diverge in passing through it, and are therefore all so nearly of the same length, and consequently in the same phase or state of undulation, that none of them interfere sufficiently to destroy one another. Hence all the particles of air in the room are set into a state of vibration, so that the intensity of the sound is very nearly everywhere the same. Strong as the preceding cases may be, the following experiment, made by M. Arago, seems to be decisive in favour of the undulatory doctrine. Suppose a plano-convex lens of very great radius to be placed upon a plate of very highly polished metal. When a ray of polarized light falls upon this apparatus at a very great angle of incidence, Newton’s rings are seen at the point of contact. But as the polarizing angle of glass differs from that of metal, when the light falls on the lens at the polarizing angle of glass, the black spot and the system of rings vanish. For although light in abundance continues to be reflected from the surface of the metal, not a ray is reflected from the surface of the glass that is in contact with it, consequently no interference can take place; which proves beyond a doubt that Newton’s rings result from the interference of the light reflected from both the surfaces apparently in contact (N.199).

Notwithstanding the successful adaptation of the undulatory system to phenomena, the dispersion of light for a long time offered a formidable objection to that theory, which has been removed by Professor Powell of Oxford.

A sunbeam falling on a prism, instead of being refracted to a single point of white light, is separated into its component colours, which are dispersed or scattered unequally over a considerable space, of which the portion occupied by the red rays is the least, and that over which the violet rays are dispersed is the greatest. Thus the rays of the coloured spectrum, whose waves are of different lengths, have different degrees of refrangibility, and consequently move with different velocities, either in the medium which conveys the light from the sun, or in the refracting medium, or in both; whereas rays of all colours come from the sun to the earth with the same velocity. If, indeed, the velocities of the various rays were different in space, the aberration of the fixed stars, which is inversely as the velocity, would be different for different colours, and every star would appear as a spectrum whose length would be parallel to the direction of the earth’s motion, which is not found to agree with observation. Besides, there is no such difference in the velocities of the long and short waves of air in the analogous case of sound, since notes of the lowest and highest pitch are heard in the order in which they are struck. In fact, when the sunbeam passes from air into the prism, its velocity is diminished; and, as its refraction, and consequently its dispersion, depend solely upon the diminished velocity of the transmission of its waves, they ought to be the same for waves of all lengths, unless a connexion exists between the length of a wave and the velocity with which it is propagated. Now, this connexion between the length of a wave of any colour, and its velocity or refrangibility in a given medium, has been deduced by Professor Powell from M. Cauchy’s investigations of the properties of light on a peculiar modification of the undulatory hypothesis. Hence the refrangibility of the various coloured rays, computed from this relation for any given medium, when compared with their refrangibility in the same medium determined by actual observation, will show whether the dispersion of light comes under the laws of that theory. But, in order to accomplish this, it is clear that the length of the waves should be found independently of refraction, and a very beautiful discovery of M. Fraunhofer furnishes the means of doing so.

That philosopher obtained a perfectly pure and complete coloured spectrum, with all its dark and bright lines, by the interference of light alone, from a sunbeam passing through a series of fine parallel wires covering the object glass of a telescope. In this spectrum, formed independently of prismatic refraction, the positions of the coloured rays depend only on the lengths of their waves, and M. Fraunhofer found that the intervals between them are precisely proportional to the differences of these lengths. He measured the lengths of the waves of the different colours at seven fixed points, determined by seven of the principal dark and bright lines. Professor Powell, availing himself of these measures, has made the requisite computations, and has found that the coincidence of theory with observation is perfect for ten substances whose refrangibility had been previously determined by the direct measurements of M. Fraunhofer, and for ten others whose refrangibility has more recently been ascertained by M. Rudberg. Thus, in the case of seven rays in each of twenty different substances, solid and fluid, the dispersion of light takes place according to the laws of the undulatory theory: and there can hardly be a doubt that dispersion in all other bodies will be found to follow the same law. It is, however, an express condition of the connexion between the velocity of light and the length of its undulations, that the intervals between the vibrating molecules of the ethereal fluid should bear a sensible relation to the length of an undulation. The coincidence of the computed with the observed refractions shows that this condition is fulfilled within the refracting media; but the aberration of the fixed stars leads to the inference that it does not hold in the ethereal regions, where the velocities of the rays of all colours are the same. Strong as all that precedes is in favour of the undulatory theory, the relative velocity of light in air and water is the final and decisive proof. By the Newtonian theory the velocity is greater in water than in air, by the undulatory theory it is less; hence if a comparison could be made it would decide which is the law of nature. The difficulty consisted in comparing the velocity of light passing through a small extent of water with the velocity of light in air, which is 10,000 times greater than the velocity of the earth in its orbit. This delicate and difficult experiment was made by means of an instrument invented by Professor Wheatstone for measuring the velocity of electricity. It consists of a small mirror which revolves in its own plane like a coin spinning on its edge. When it revolves very rapidly the reflected image of an object changes its place perceptibly in an inconceivably small fraction of a second. The mirrors used in the experiment were made to revolve more than 1000 times in a second, by which means the places of the two images—one from light passing through air, and the other from light passing through an equal length of water—were found to be such as to prove that the velocity of light in air and in water is as 4 to 3, while by the Newtonian theory it is as 3 to 4. By this final and decisive proof the undulatory theory may from henceforth be regarded as the law of nature. This experiment was accomplished by M. Fizeau and M. LÉon-Faucault, at the suggestion of M. Arago, whose eyesight did not permit him to undertake it himself.