Atmospheric optics is the branch of physics that explains how light interacts with water droplets and ice crystals suspended in the atmosphere to produce phenomena like rainbows, halos, coronae, and glories. The primary rainbow forms when sunlight enters a spherical water droplet, undergoes one internal reflection, and exits: red light (n ≈ 1.331 at 700 nm) exits at a minimum deviation of 42.3° from the anti-solar point, while violet (n ≈ 1.344 at 410 nm) exits at 40.6°, spreading the spectrum across a 1.7° wide arc with red on the outside. The secondary rainbow at ~51° involves two internal reflections, reversing the colour order and reducing brightness by a factor of about three. Between 42° and 51° lies Alexander's dark band — a region where no rainbow rays reach the observer, making the sky noticeably darker.
Ice-crystal halos form by a completely different mechanism: refraction through the flat prism faces of hexagonal ice crystals in high cirrus clouds. The 22° halo arises from rays passing through two prism faces at the 60° apex angle — the minimum deviation for water ice (n ≈ 1.310) is 21.8°, so most light accumulates at this radius, creating a bright ring with a dark interior. The rarer 46° halo uses the 90° prism formed by a prism face and a basal face. This simulation lets you explore both phenomena together: switch between Rain, Ice, and All modes to compare how geometric optics with Snell's-law refraction and internal reflection generates the vivid colours you see in the sky.
The primary rainbow appears at ~42° from the anti-solar point because that is the angle of minimum deviation for a light ray that enters a spherical water droplet, undergoes one internal reflection, and exits. Red light (n ≈ 1.331) has its minimum deviation at 42.3°, while violet (n ≈ 1.344) exits at 40.6°, spreading the colours across about 1.7°.
The secondary rainbow forms from rays that undergo two internal reflections inside the droplet. Each extra reflection adds a path-reversal, so the colour order is reversed — violet appears on the outside at ~53° and red on the inside at ~51°. Two reflections also cost more light, making the secondary bow about three times fainter than the primary.
Between 42° and 51° there is a region called Alexander's dark band where no rainbow rays reach the observer — primary rays all exit below 42° and secondary rays all exit above 51°. The sky inside the primary bow appears brighter because scattered light from the droplets reaches the observer from those directions, while Alexander's band receives no such light.
The 22° halo arises when sunlight refracts through two prism faces of randomly oriented hexagonal ice crystals. The 60° apex angle of the prism gives a minimum deviation of ~21.8° for water ice (n ≈ 1.31). Rays cannot exit at smaller angles because they undergo total internal reflection, so light accumulates at this minimum, producing a bright ring with a dark interior.
The 46° halo forms when light enters through a prism face and exits through the basal (flat top/bottom) face of a hexagonal ice crystal, giving a 90° prism angle instead of 60°. The minimum deviation for a 90° prism is ~45.7°. This halo is rarely seen because it requires a specific crystal geometry and typically appears much fainter than the 22° halo.
Mie scattering is the exact electromagnetic solution for scattering by spherical particles of any size, including raindrops. For large droplets (radius much greater than wavelength), Mie theory converges to geometric optics and predicts the same 42°/51° rainbow angles. Mie scattering also predicts supernumerary bows — narrow interference fringes just inside the primary rainbow caused by wave interference between rays taking different paths through the droplet.
Rainbows appear in the part of the sky directly opposite the sun — the anti-solar point. The minimum-deviation angles (42° for primary, 51° for secondary) are measured from the anti-solar point outward. If the sun is above 42°, the primary bow falls below the horizon and cannot be seen from the ground; circular rainbows are only visible from aircraft or elevated positions.
Larger droplets (radius above 1 mm) produce vivid, narrow, bright rainbows with well-separated colours. Smaller droplets (drizzle, fog, radius below 0.1 mm) produce fogbows — broad, nearly white arcs — because diffraction becomes significant relative to refraction. Very small droplets produce a featureless white arc as colour spreads merge together.
Yes. Ice has wavelength-dependent refractive index, so red light (n ≈ 1.306) bends less than violet (n ≈ 1.318). At the inner edge of the 22° halo, red appears first, giving the characteristic reddish-orange inner rim. The colour spread in ice halos is similar to that in rainbows, though halos often appear whiter overall because dispersion in ice is weaker than in liquid water.
Rainbow brightness depends on droplet size (larger droplets give a brighter primary), droplet number density (more drops equals brighter bow), the sun's elevation angle, and the refractive index of water. Fresnel reflection losses at each droplet surface reduce brightness further, and the secondary bow loses an additional factor of roughly three due to the second internal reflection and partial polarisation effects.