Fresnel and Snell at an Interface

Reflection and refraction at a planar dielectric interface. The refracted beam bends by Snell, the Fresnel equations fix the s- and p-reflectance, the reflected p-beam vanishes at Brewster theta_B = atan(n2/n1), and from a dense to a rare medium beyond the critical angle the wave is totally internally reflected with an evanescent skin. Energy is conserved, R + T = 1. The primary scene is the physical interface with incident, reflected and refracted beams whose width tracks the power and a polarization-state inset; the side panel is the Fresnel R_s, R_p versus angle with the Brewster and critical markers.