Understanding wave characteristics via linear superposition of retarded fields

The Feynman–Schwartz method of linearly superposing retarded fields to understand the origin of the refractive index is generalized to an obliquely incident electromagnetic wave interacting with a planar medium. Different integral equations for the wave field in the medium are obtained for the TE-state and the TM-state of wave polarization. The two states of polarization are shown to satisfy the same differential equation for the spatial variation of the fields and thus they have the same dispersion relation (or the index of refraction) and change of phase velocity upon penetration into the medium. The integral equations are also used to deduce the well-known reflection and transmission coefficients in various cases.