Relationship between the p and s Fresnel reflection coefficients of an interface independent of angle of incidence

The Fresnel reflection coefficients rp and rs of p- and s-polarized light at the planar interface between two linear isotropic media are found to be interrelated by (rs − rp)/(1 − rsrp) = cos 2β, independent of the angle of incidence ϕ, where tan2β = ∊ and ∊ is the (generally complex) ratio of dielectric constants of the media of refraction and incidence. This complements another relation (found earlier), (rs2 − rp)/(rs − rsrp) = cos 2ϕ, which is valid at a given ϕ independent of ∊ (i.e., for all possible interfaces). Taken together, these two equations specify rp and rs completely and can be used to replace the original Fresnel equations.