Short answer
Sunlight refracted into a raindrop, reflected once off the back and refracted out again concentrates at about 40–42° from the point directly opposite the sun, with each wavelength at a slightly different angle, so the colours spread into a ring. A second reflection makes a fainter, colour-reversed bow about 10° further out; the faint pastel bands inside the main bow are supernumeraries, produced by interference.
Light entering a spherical drop at different heights leaves at different angles after one internal reflection, but the exit angles pile up near a maximum deviation — a caustic — so most returning light is concentrated around one angle from the antisolar point, the shadow of your head. For water, that is about 40–42°. Because the index of refraction varies slightly with wavelength, red concentrates at the larger angle and violet at the smaller, so red is on the outside of the primary bow. The bow is really a cone of light with its axis through your eye: every observer sees their own rainbow from a different set of drops, which is why you can never reach its end.
Light that reflects twice inside the drop forms a secondary bow about 10° further from the antisolar point, near 50–52°. The extra reflection reverses the order, so red is on the inside, and loses more light, so it is fainter. Between the two bows, no singly or doubly reflected light is sent to the observer, so that region of sky is slightly darker than the sky outside the secondary — Alexander's dark band. Inside the primary bow the sky is brighter than outside, because light deviated less than the maximum still reaches the eye there.
Just inside the primary bow, faint alternating pink and green bands sometimes appear. These supernumerary bows cannot be explained by rays. Two rays can leave a drop in the same direction after travelling different paths inside it, and when they meet they interfere, reinforcing at some angles and cancelling at others. Thomas Young used this in the early nineteenth century as evidence that light is a wave; George Airy developed his function in 1838 to describe the intensity across the bow more accurately. Supernumeraries are clearest when drops are small and uniform in size, since mixed sizes blur the fringes.
Each wavelength forms its own bow with a finite width, and the sun is a disc about half a degree across rather than a point, so the bows for neighbouring wavelengths overlap and every point on a rainbow is a mixture. That is why the bands are soft, why the colours are less saturated than spectral colours from a prism, and why the middle bands can be hard to name. With very small drops — in fog or mist — diffraction broadens each colour so much that they overlap entirely, giving a white fogbow. The seven named colours are a convention covered on the site's visible spectrum page.
| Feature | Where | Cause |
|---|---|---|
| Primary bow | About 40–42° from the antisolar point, red outside | One internal reflection plus dispersion |
| Secondary bow | About 10° further out, colours reversed | Two internal reflections |
| Alexander's dark band | Between the two bows | No once- or twice-reflected light sent there |
| Supernumerary bows | Just inside the primary | Interference between paths through the drop |
| Fogbow | Same angle, nearly white | Tiny drops broaden each colour until they overlap |
Each statement is labelled by kind — established fact, a standard’s requirement, observed market data, a convention, or Colourwise’s own interpretation or analysis — with the strength of the evidence behind it.
FactStrong evidence
The primary rainbow forms about 40–42° from the antisolar point; the secondary bow lies about 10° further out with its colours reversed, and the sky between the two is slightly darker.
Source: HyperPhysics (optics, atmospheric optics and vision pages)
FactStrong evidence
Supernumerary bows are produced by interference between light rays traversing a raindrop by different paths and emerging in the same direction; Airy introduced his function in 1838 to describe the rainbow's intensity profile.
Source: Digital Library of Mathematical Functions, Sidebar 9.SB1: Supernumerary Rainbows
FactModerate evidence
Supernumerary arcs are most distinct when drops are small and uniform in size, because a range of sizes shifts the interference fringes and blurs them.
Source: Digital Library of Mathematical Functions, Sidebar 9.SB1: Supernumerary Rainbows; Wikipedia (biology, ecology, mineralogy and earth-science articles)
Reviewed 29 September 2026. Colourwise summarises its sources in its own words and does not reproduce standards text or proprietary colour data. Spotted an error? Tell us.