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.