Particle approach to the Fresnel coefficients

Abstract

The Fresnel reflectivity and transmissivity coefficients for a semi-infinite medium are derived for normal and oblique incidence using a particle approach and a probabilistic condition at the boundary. The method depends in part on the behavior of the momentum of light in ordinary refractive media, and this subject is discussed. The method clarifies why the Schr\"odinger equation for the comparable problem (potential-step) and Maxwell's equations yield the same coefficients for normal incidence. The use of the phase velocity rather than the group velocity in formulating the probabilistic condition is interpreted from a quantum viewpoint, although the absence of Planck's constant in the analysis suggests one is dealing with a kind of nonclassical but prequantal indeterminacy. An analysis and review of the momentum, inertia, and energy-momentum tensor of light in ordinary refractive media is also given.