The condition that the ratio of the intensities of the transmitted and reflected electric waves at the interface between two media is independent of their plane of polarisation

Abstract

It has been shown that the condition that a steady state of electrical oscillations can be set up in a comparatively short time in a space, whose outer boundary separates two dielectric media with different electric constants, is that the ratio of the specific inductive capacities of the two media is approximately equal to the ratio of the magnetic permeabilities. This suggests that, when the ratios are equal, the ratios of the incident, transmitted, and reflected disturbances are independent of the direction of the plane of polarisation of the incident disturbance, and this can be readily verified. The object of the present communication is to prove that the condition is necessary, that is, the condition that the ratios of the intensities of the incident, transmitted, and reflected electric waves at the interface between two media is independent of the direction of the plane of polarisation of the incident waves is that the ratio of the specific inductive capacities of the two media is equal to the ratio of the magnetic permeabilities of the two media. Taking the plane of separation of the two media to be the plane z = 0, let K, μ be the specific inductive capacity and the magnetic permeability respectively of the medium for which z > 0, and let K', μ' be the specific inductive capacity and the magnetic permeability of the medium for which z ˂ 0, and let the electric force in the incident waves be given by (A, B, C) e tk ( lx+my+nz +V t ) , where A l + B m + C n = 0, KμV 2 = 1;