SNELL
n₁sinθ₁ = n₂sinθ₂ — and past the critical angle, a perfect mirror.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A ray of light arrives at the border between two media — air above, glass below, or any pair you choose. The crossing has rules, the rules have one line, and the line was worth a scientific revolution.
Wavefronts
Light is slower where n is larger, and the wavefronts must stay stitched together at the border. So one flank of the marching column shortens its stride before the other — and the whole column wheels. Refraction is a marching band turning on wet grass.
Solve
Stitching wavefronts across the border compresses into one line: n₁sinθ₁ = n₂sinθ₂. Solve for θ₂ and check the answer exists — when sinθ₂ would exceed 1, refraction is cancelled and the surface becomes a perfect mirror.
Cross
A pulse makes the crossing, slowed a hundred-million-fold. Different indices permit transmitted and reflected components; matched indices have no optical boundary and therefore no reflected pulse. The drawing suppresses that component exactly when n₁ = n₂.
Audit
The invariant n sinθ matches across the border to machine precision, and running the ray backward returns it along the identical path — reversibility, audited. Where no transmitted angle exists, the critical angle stands guard: past it, the light is trapped, and fiber optics says thank you.