Chapter 5.3, Problem 73E

APPLICATIONS

Rainbows Rainbows are created when sunlight of different wavelengths (colors) is refracted and reflected in raindrops. The angle of elevation $\theta$ of a rainbow is always the same. It can be shown that $\theta =4\beta -2\alpha ,$ where

$\sin \alpha =k\sin \beta$

and $a=59.4°$ and $k=1.33$ is the index of refraction of water. Use the given information to find the angle of elevation $\theta$ of a rainbow. [Hint: Find $\sin \beta ,$ then use the $\boxed{SI{N}^{-1}}$ key on your calculator to find $\beta .]$ (For a mathematical explanation of rainbows see Calculus Early Transcendentals, $7th$ Edition, by James Stewart, page $282.)$