The Theory of the Reflectivity of Metals

The reflectivity of an ideal metal is calculated for infra-red light by a quantum-mechanical method. It is assumed that the conduction electrons in the metal absorb light by a photoelectric process which takes place near the surface, that these electrons behave as if they are free and that the light within the metal decays according to the formula given by the classical skin effect. Two types of wave functions are assumed for the electrons, corresponding to the assumptions of specular and diffuse reflection of the electrons at the surface of the metal. The absorptivity (1- R , where R is the reflectivity) in the case of specular electron reflection is found to be A S = ( Ne 2 /2πmν 2 ) ν 0 3 / c 3 ; for diffuse reflection, A D = fraction three-quartersν 0 / c . These results are the same as those obtained by Holstein and by Dingle using different methods which are essentially classical. Since A D gives the better agreement with experiment, it is concluded that the `diffuse reflection' wave functions are a better approximation to the exact electronic wave functions that the `specular reflection' wave functions which have been used in previous work on the photoelectric effect and reflectivity.