Correlation of Fresnel's interface reflection coefficients of external and internal reflection at the same angle of incidence for dielectric-dielectric interfaces

The pair of Fresnel amplitude reflection coefficients for internal and external reflection, that apply when p- polarized light is incident on an interface between two transparent media form opposite sides at the same angle of incidence, are considered jointly and plotted together. This creates an interesting family of curves, with the angle of incidence as a parameter. Besides the well known characteristics of total reflection at the critical angle and total refraction at the Brewster angle, some unusual properties become apparent that pertain to light reflection at the special angles of 45 degrees and 51.827 degrees. The Stokes relations apply strictly at normal incidence, and approximately at other angles for nearly vanishing interfaces. The corresponding result for the Fresnel reflection coefficient for the s polarization, and for the ratio of p and s reflection coefficients, are also obtained.