The Rainbow

single droplet — caustic of minimum deviation

sky — antisolar point, 42° / 51° double bow

Trace parallel sunlight through one spherical drop at every impact parameter b. Snell bends it in, it reflects inside, Snell bends it out. Light piles up at the angle of least deviation — a caustic — and that bright ray is the rainbow. Repeat across the sky and the bow appears.

Single drop

Impact parameter b 0.86

Sky

Sun elevation 10°

Skin

Drag on the drop view to set b. The D(b) plot marks the minimum — the Descartes ray. Colours are true wavelength→sRGB, so red sits outside violet on the primary and the order flips on the secondary. The gap between them is Alexander's dark band.