The reflexion and transmission of electric waves at the interface between two transparent media

Abstract

The effect of a transparent sphere on a train of plane waves has been fully investigated by Lorentz in an important paper. The object of the present communication is to obtain approximate expressions for the electric and magnetic forces in the transmitted and in the reflected waves, where electric waves are incident on the interface between two media, the surface of separation being any surface. In a former paper the writer investigated in particular the case of a perfectly conducting obstacle, and the method adopted for that purpose will be applied in the present case. The assumption is that the most important parts of the electric and magnetic forces in the transmitted and reflected waves are due to the magnetic and electric distributions at any point on the separating surface which would produce the electric and magnetic forces in the immediate neighbourhood of the point if the surface were a plane surface. The equations which express the magnetic and electric forces at a point in terms of the magnetic and electric current distributions are:—