The 22° Halo: Why a Bright Ring Circles the Sun

The setup: sunlight, ice, and a 60° prism

On a day when a thin veil of cirrostratus whitens the sky, sunlight is passing through millions of tiny hexagonal ice crystals — pencil-shaped columns and flat plates a few tenths of a millimetre across. A hexagonal prism has six long side faces; any two alternate faces meet, when extended, at a 60° apex, so a ray that enters one side face and leaves the second-next face is refracted exactly as if it had crossed a 60° glass prism. Ice bends light with refractive index n ≈ 1.31, and the fixed geometry of that bending is what paints a luminous ring at one precise angle around the Sun.

Minimum deviation: why the light piles up at 22°

A prism does not bend every ray by the same amount. The total deviation D — the angle between the incoming and outgoing ray — depends on how the ray strikes the crystal, and it has a minimum. For a prism of apex A and index n, that minimum satisfies

n = sin((A + D_min)/2) / sin(A/2)

With A = 60° and n = 1.31 this gives D_min ≈ 21.8°. The key is what happens near that minimum: as a crystal tumbles, its orientation sweeps the incidence angle through a wide range, but D changes very slowly close to its minimum. A huge span of orientations therefore funnels light into a narrow band of deviation right at 21.8° — an optical pile-up called a caustic. And crucially, no orientation deviates light by less than 21.8°, so no refracted sunlight lands inside that angle. The result is a ring with a sharp bright inner edge, a darker disk of sky inside it, and a gentle fade outward.

A worked example: where 21.8° comes from

Follow the symmetric ray — the one at minimum deviation, which crosses the crystal parallel to its base:

1. By symmetry the ray refracts equally at both faces, so inside the ice it makes an angle r = A/2 = 30° with each face's normal.
2. Snell's law at the entry face: sin i = n · sin r = 1.31 × sin 30° = 0.655, so the incidence angle i = 40.9°.
3. Each face bends the ray by i − r = 40.9° − 30° = 10.9°.
4. Two faces double it: D_min = 2 × 10.9° ≈ 21.8°.

That single number — set only by the 60° geometry of ice and its refractive index — is the radius of the halo. Rays that strike more steeply or more shallowly are all thrown outside 21.8°, which is why the ring is not a thin line but a band that brightens abruptly at its inner rim.

Color, width, and the sharp inner edge

Because n depends on wavelength, the minimum-deviation angle differs slightly for each colour. Ice refracts blue (n ≈ 1.317) a touch more than red (n ≈ 1.307), so the red minimum sits near 21.6° and the violet near 22.4°. Red is deviated least and forms the inner edge of the ring, closest to the Sun — the reverse of a rainbow's order. The whole coloured spread is under 1°, and the finite Sun (0.53° across) smears each colour by about half a degree, so the tints overlap and mostly wash out. The eye sees a largely white ring with a distinct reddish inner rim and a bluish-white outer glow — never the vivid banding of a true rainbow.

Why a full ring? Random orientation vs. sundogs

A closed ring requires the crystals to be randomly oriented — tumbling every which way — so every rotational orientation is represented and light emerges at 21.8° all the way around the Sun. This is the condition people most often overlook. If instead the crystals are flat plates settling with their broad faces horizontal (as larger, slower crystals do in still air), the 60° geometry is sampled only in a horizontal plane. The light then concentrates into two bright, often coloured patches at the same altitude as the Sun and about 22° to either side — sundogs (parhelia), not a ring. Same prism, same 22°; different crystal orientation, completely different picture. Horizontal-axis columns instead build the bright upper tangent arc perched on top of the halo.

History, folklore, and where you see it

Halos are among the oldest recorded sky phenomena — Aristotle noted them, and a famous 1629 display over Rome prompted Descartes to write about halos in his 1637 Les Météores. The correct ice-crystal refraction explanation is usually credited to Edme Mariotte in the 1680s; the full geometry, including the precise 21°50′ radius and the 46° halo, was worked out by Auguste Bravais around 1847. Halos are far more common than rainbows — seen on the order of a hundred days a year in many climates, whenever high cirrus drifts across the Sun or Moon (a lunar halo is the identical effect, merely dimmer). The saying "ring around the Moon means rain" even has real physics behind it: the cirrostratus that makes halos often runs ahead of an approaching warm front, so a halo genuinely can precede a change in weather — though far from reliably.

How the 22° halo compares with the primary rainbow and its larger, rarer cousin, the 46° halo.

Feature	22° Halo	42° Rainbow (primary)	46° Halo
Refracting particle	Hexagonal ice crystals	Spherical water drops	Hexagonal ice crystals
Light path	Refraction only, 60° prism	Refraction + 1 internal reflection	Refraction only, 90° prism
Angular radius	≈ 21.8°	≈ 42°	≈ 46°
Where in the sky	Ring centered on the Sun	Arc opposite the Sun	Larger ring on the Sun
Color order	Red on the inner edge	Red on the outer edge	Red on the inner edge
How often seen	Common (~100 days/yr)	Common after showers	Rare and faint