On the Reflection of Light at 45° Angle of Incidence

Abstract
When light is incident at an angle of 45° on the interface between a transparent medium and an absorbing medium, the complex amplitude reflection coefficients r p and r s for the p and s polarizations are related by r p = r s 2. It follows that the intensity reflectances are similarly related, i.e. R p = R s 2 where R = S r S 2, as has been previously noted, and that the reflection phase shift for the p polarization is double that for the s polarization, i.e. i p = 2 i s where i = arg r, which, as far as can be ascertained, is a new result. Two other interesting consequences of light reflection at 45° are that (1) ellipsometry at this angle determines the complex reflection coefficient r s in both magnitude and phase, and (2) the angular beam deviation on refraction when both media are transparent is equal to the polarization (or ellipsometric) angle. This is one of the simplest possible relations between propagation directions and polarization directions, i.e. between two properties, one related to geometrical optics and the other to physical optics.