Total internal reflection · critical angle

Send light the other way — from dense glass UP into air. It bends away from the normal, but can it always escape? Is there an angle past which none gets out?

▶ Run the simulationSee the measured result

Units: critical angle θ_c = asin(n₂/n₁) = asin(1/1.5) = 0.7297277 rad = 41.8103149° for crown glass n₁ = 1.500 → air n₂ = 1.000; Hecht, Optics 5e, §4.7

How the lab tests it

Sweep the incidence angle θ₁ for light going glass (n₁=1.5) → air (n₂=1.0). At each angle draw the incident, reflected and refracted rays, dimming each by its Fresnel share of the energy. The on-screen critical angle is EARNED, not looked up: the module races light down broken glass→air paths (the only physics coded is travel time t = n·length per leg), locates each least-time crossing by golden-section on time comparisons, measures the winners' sines from their segments, and extrapolates the through-origin line sinθ₁ = a·sinθ₂ to grazing (sinθ₂ = 1) — that incidence IS the critical angle.

What it checks

SNELL + the CRITICAL ANGLE — θ₂ = asin((n₁/n₂)·sinθ₁) climbs to 90° at θ_c = asin(n₂/n₁) = 41.8°, beyond which sinθ₂ > 1 is impossible: NO transmitted ray exists and the reflection is total (the timed-race θ_c matches asin(n₂/n₁) to 3.8e-8 — the whole gap is the sqrt(eps) golden-section comparison basin, and both render as the identical 41.81°)

Critical angle calculator

Past the critical angle nothing refracts out — the interface becomes a perfect mirror. Total internal reflection needs the light to start in the denser medium (n₁ > n₂).