🔻 2D Snell's Law — Refraction, TIR & Fresnel Intensity

The 3D version renders the same ray geometry in WebGL but only shows angles. This 2D version adds a real Fresnel-equations solver, so it plots exactly how much of the light's intensity is reflected versus transmitted at every incidence angle, not just where the rays point.

They are the exact solutions of Maxwell's equations at a flat dielectric interface for the s-polarized and p-polarized reflection amplitudes: r_s = (n₁cosθ₁ − n₂cosθ₂)/(n₁cosθ₁ + n₂cosθ₂) and r_p = (n₂cosθ₁ − n₁cosθ₂)/(n₂cosθ₁ + n₁cosθ₂). Squaring and averaging them gives the unpolarized reflectance R, and energy conservation gives the transmittance T = 1 − R.

Once the incidence angle exceeds the critical angle (only possible when n₁ > n₂), there is no real refraction angle, the Fresnel formulas give |r|² = 1, and the plotted reflectance R jumps to exactly 100% while transmittance drops to 0% — all of the incident power returns into medium 1.

Whenever n₁ ≠ n₂, the denominators and numerators in the Fresnel formulas aren't equal, so r_s and r_p are nonzero even at normal incidence (θ₁=0°). For an air-to-glass boundary that works out to about 4% reflectance, which is why uncoated glass and camera lenses show a faint reflection.

Yes for both parts: the ray angles follow Snell's law and the critical-angle formula exactly, and the intensity split follows the full unpolarized Fresnel equations (not an approximation), assuming both media are lossless dielectrics and the beam is a plane wave.