REFRACTION & REFLECTION

n₁sinθ₁ = n₂sinθ₂ — and past the critical angle, a perfect mirror.

Three rays, one meeting point — geometry and algebra agree to the last digit.

Same equation as the lens — light forgets whether it bent or bounced.

Snell twice per color — and at minimum deviation, the prism measures its own glass.

Darkness made of light — d·sinθ = mλ, and only ⌊d/λ⌋ fringes exist.

The bow is a caustic — dD/dθ = 0 on a sphere: red 42.3° outside violet 40.6°, and a dark band above.

Ice prisms at minimum deviation — the 22° ring around the sun, red on the inside, exact to 1e-12.