Dispersion

Dispersion is the dependence of a material's refractive index on wavelength. Glass slows blue light slightly more than red, so blue refracts more steeply at each surface. A prism exploits this twice, at entry and exit, spreading white light into a spectrum; the same property causes chromatic aberration in lenses, which designers quantify with the Abbe number.

A rainbow is dispersion in raindrops. Light enters a drop, refracts, reflects once off the back surface, and refracts again on the way out. The deviation angle depends on where the ray strikes the drop and has a maximum; rays pile up near that limit, concentrating brightness into an arc instead of smearing it across the sky. The limit lies near 42° from the antisolar point for red and near 40° for violet, so a bow always appears at a fixed angle from the observer's own shadow, and every observer sees a different bow.

Red on the outside follows from those angles. A drop delivering red light to the eye lies on a slightly wider cone than one delivering violet. In the fainter secondary bow, produced by two internal reflections, the order reverses.

The popular explanation — that the outer band is longer, like the outer lane of a running track, so something must travel further — is memorable but is not the mechanism. Nothing races around the arc; the ordering comes entirely from wavelength-dependent refraction inside individual drops. It is a tidy Plausible Mechanism: right picture, wrong reason, no substitute for Ground Truth.

Rainbow light is also strongly polarized by the internal reflection, so it dims under a rotating filter; see Polarized Light. And the spectrum contains no magenta, which is not a wavelength but a perceptual construct — see Opponent Process Theory.