The optical properties of solids

1—The theory of the optical constants of metals remained in the state in which it was left by Drude until Kronig applied the modern theory of metals to the problem. Since the appearance of Kronig's first paper many authors have tried to extend the theory so as to bring the finer effects within its scope, and we may sum up the present position as follows. In the infra-red the optical constants of metals vary with temperature, and are therefore very much influenced by the thermal vibrations of the solid. For frequencies in this region the existing theory is effectively the Drude theory which relates the optical constants to the conductivity in static fields and to the inertia of the electrons. This theory is satisfactory in the far infra-red, but fails in the near infra-red. In the visible and ultra-violet the optical constants are approximately independent of temperature, which means that the effect of the theory to be reasonably accurate, and we might hope to obtain useful information about the internal state of a metal. It must, however, be admitted that there is no really consistent theory extant, and, since our means of investigating the interior of a metal are very limited indeed, it seems desirable that the theory should be put upon as sound a basis as possible. It is the main object of this paper to give a critical discussion of the phenomenon in the visible and ultra-violet, the effect of the lattice vibrations being entirely neglected. In 2 the fundamental formula, which is a generalization of the Kramers-Heisenberg dispersion formula, is derived, and it shown that it is quite unnecessary to make the wave-length. In fact the problem becomes clarified if we do not make this assumption. It is also shown that there is no Lorentz-Lorenz correction to be introduced.