—When light falls on an atom it sets the electrons in motion and they therefore re-emit light, and the character of this scattered light will depend on the nature of the atom as well as the incident light. But the effect of a single atom is too small to be observable, so that we always have to use a large number and the compounding of their effects produces complications. In fact the scattering of light by matter is a more primitive quality than is refraction, and it is therefore best to reduce everything into terms of scattering before we approach the theory of the behaviour of the single atom. There are several different ways in which an atom may emit light under the stimu lus of light, but we can exclude some of them from consideration. Thus certain substances respond by fluorescing, that is to say emitting light of a different wave-length, and again there is the important phenomenon of resonance radiation (.vi).) where the wave-length of the light is unaltered, but where it appears that there is no phase relation between the incident and the scattered light. (See PHOSPHORESCENCE AND FLUORESCENCE.) Both these phenomena are extremely interesting, but from the present point of view they may be regarded as an absorption and simultaneous re-emission of the light, and so they belong to the theory of the emission of light and are outside our scope.
The most universal way in which atoms react to light is by the emission of waves of the same frequency and having a definite phase relation to the incident light, and this process, to which we shall limit the name of scattering, is responsible for refraction, both ordinary and double, and for gyration. In order that all these effects may be explained, we can see one property which the scat tered waves must always have. The various refractive effects are all due to an interference between the original and the scattered waves, and, since the refraction is independent of the brightness of the light, it follows that the wave scattered by an atom, what ever its other characters, must be proportional in amplitude to the incident force. Another of its properties depends on the fact that for ordinary light the wave-length of the light is always far greater than the size of the atom; hence at any instant the atom is practically in a uniform field of force, and so the scattered wave will depend only on the polarization and frequency of the incident wave, but not at all on the direction of its wave-front. These conditions must hold for any atom, but apart from them there is great liberty of choice for the form of the scattered spherical wave. We shall see that for some purposes we have to assume circle-waves and screw-waves, but both ordinary and double refraction are fully accounted for by means of ordinary line-waves; moreover for transparent substances the line-wave is exactly in phase with the incident. All these results can be de
duced by assuming completely general types of spherical waves and then seeing what limitations will give rise to the various re fractive effects, but here we shall pursue the opposite course and shall assume the form of the scattered wave and show that our assumption is verified. For the most important case, that of the re fraction of a transparent medium, we can summarize our assump tions in the form that under incident light of amplitude
the wave scattered by an atom is a line-wave of the form we gave with
written for A, and with pole along the direction of Eo. Then p, which depends only on the nature of the atom and on the frequency of the incident light, is the scattering constant of the atom.
The most primitive exhibition of scattering is not found in refraction, but in such phenomena as the light of the sky (q.v.), and it is therefore appropriate to dis cuss this first. Supposing that the observer looks at a point not very near the sun, the light that he sees will have been scattered through a broad angle, and the phase of the light-path, sun—atom —observer, will be different for each atom. Consequently the waves from the separate atoms do not reinforce one another. If the atoms were arranged with perfect regularity their waves would arrive at the eye with regular differences of phase and would destroy one another so that the sky would look black; however the uniform density of gases is not due to systematic regularity, but to the unsystematic regularity produced by the enormous number of atoms. The atoms of a gas have no ordered positions, as they have in a crystal, hence the brightness of sky light will depend on compounding a large number of similar waves of quite arbitrary phases and taking the average value of the result. Con sider a set of n atoms each of which is giving a wave of the same magnitude, but with phases ei, €2, . . . E„. The resultant ampli tude will be proportional to
. .
and the intensity is the square of this. Now the square will consist of terms like
and others like
The latter of these are as likely to be negative as positive, so that they will average out, but the former has average value
for each separate term. Thus the average intensity scattered by the n atoms is just n times that scattered by one. If then we want to know the bright ness of the sky we only require to calculate the intensity scat tered by a single atom and multiply by the number of atoms in the field of view.