Generalised Fresnel´s law for loss due to curvature

Many rays, predicted by Fresnel´s laws to be totally reflected from a curved interface between two dielectric media, are only partially reflected. We derive a generalised Fresnel transmission coefficient to account for this loss. Our transmission coefficient applies to an arbitrary surface; e.g. one defined by two arbitrary radii of curvature. It can be used to determine radiation loss from bent and straight circular optical fibres.