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 ø, where tan2β = ∊ and ∊ is the (generally complex) ratio of dielectric constants of the media of refraction and incidence. This complements another relation (found earlier), (r2s - rp)/(rs - rsrp) = cos 2φ, which is valid at a given ø 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.
Journal of the Optical Society of America A
R. M. A. Azzam, "Relationship between the p and s Fresnel reflection coefficients of an interface independent of angle of incidence," J. Opt. Soc. Am. A 3, 928-929 (1986)