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.

Figure 1. Incident, reflected and refracted beams at a dielectric interface with the Fresnel reflectance.

WHAT TO TRY

Sweep the incidence angle: the refracted beam bends by Snell n1 sin(theta1) = n2 sin(theta2), and the Fresnel reflectance curves below track how much s and p light reflects at each angle.
Find Brewster angle, where the p-reflectance hits zero: the reflected p-polarised beam vanishes entirely, which is why polarising sunglasses kill glare off water and roads.
Raise the index ratio n2/n1: the refraction is stronger and Brewster shifts. Go the other way, from dense to light, and total internal reflection appears past the critical angle.