Great Calculations by Colin Pask

Author:Colin Pask
Language: eng
Format: azw3
ISBN: 9781633880290
Publisher: Prometheus Books
Published: 2015-07-28T00:00:00+00:00

Figure 9.3. Reflection and refraction at the interface between two materials with refractive indices n1 and n2. The incidence angle is θ1, and the refracted angle is θ2. Figure created by Annabelle Boag.

The ray incident on the raindrop forms the angle α; then the refraction angle β, and the rainbow angle γ follow from the laws of optics and a little geometry as

Finding the appropriate angle α is a technical problem that involves first considering all possible rays and then identifying those that give the dominant contribution to the rainbow. This leads to the caustic ray (details may be readily found in the fine expository article by Casselman and in the paper by Nussenzveig). The result is that we must set

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