Rainbow and dispersion

Problem

A rainbow shows colours from violet (inner) to red (outer). Why is violet on the inside and not the outside?

Solution

Chromatic dispersion. The refractive index of water depends on wavelength: it is greater for violet (short wavelength) and smaller for red. Since a greater $n$ means greater deviation, violet is refracted more than red as it passes through the droplet.

Geometry of the droplet. In each droplet the light enters, reflects internally and exits. Because of the greater deviation, violet emerges at a smaller angle (about $40^\circ$) than red (about $42^\circ$), measured from the direction of sunlight.

Position in the arc. The observer, with the Sun behind them, sees each colour coming from the droplets that send it at the right angle. Red, at the larger angle, arrives from higher droplets → outer arc; violet, at the smaller angle, from lower droplets → inner arc.

$\ev{\text{Violet has greater } n \to \text{more deviated } \to \text{smaller exit angle } \to \text{inner arc.}}$

Linked atoms

Topics: Ottica Concepts: Dispersione cromatica Skills: Analisi di casi limite e fantafisica