22° Sun Halo — Ice Crystal Refraction (2D)

Halo Rings

Sun elevation 25°

Ray Geometry

Incidence angle θᵢ 31.0°

Drag the slider — deviation angle changes as the ray sweeps the crystal face.

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Refraction r₁

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Exit angle i₂

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Deviation D

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Minimum Dₘᵢₙ

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How it works

A hexagonal ice-crystal column refracts sunlight twice: once entering a side face, once leaving another face at apex angle A to the first (A ≈ 60° for the common 22° halo; A ≈ 90° when light exits the crystal's flat basal end instead, giving the fainter 46° halo). For refractive index n ≈ 1.31 and incidence angle θᵢ, Snell's law twice gives the total deviation:

D(θᵢ) = θᵢ + i₂ − A, where r₁ = asin(sin θᵢ / n), r₂ = A − r₁, i₂ = asin(n·sin r₂)

D(θᵢ) is not monotonic — it dips to a minimum at the symmetric path (r₁ = r₂ = A/2) and rises on either side. Crystals tumbling randomly in the air present every incidence angle equally, but because D is flat near its minimum, a disproportionate share of exit rays pile up at almost exactly D_min — D_min ≈ 22.0° for A = 60° and ≈ 45.9° for A = 90°. That pile-up is the halo: a bright ring at a fixed angular radius from the sun, with darker sky just inside it (no ray deviates less than D_min) — the same reason a rainbow has a sharp edge. The ring shows a faint red-inside/blue-outside fringe because ice bends violet light slightly more than red.

Sun 22° ring 46° ring

Prism ray-trace & deviation curve D(θᵢ)