Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 33 - Electromagnetic Waves - Problems - Page 1005: 62b

Answer

If the fish descends, then the diameter of the circle increases.

Work Step by Step

We can use Equation (33-45) to find the critical angle $\theta_c$ at the interface between water and air: $\theta_c = sin^{-1}~\frac{n_2}{n_1}$ $\theta_c = sin^{-1}~\frac{1.00}{1.33}$ $\theta_c = 48.75^{\circ}$ The maximum refraction angle of the light as it enters the water is $48.75^{\circ}$ Let $D$ be the depth of the fish in the water. We can find an expression for the radius of the circle: $\frac{r}{D} = tan~48.75^{\circ}$ $r = D~tan~48.75^{\circ}$ We can see that as the depth increases, then the radius also increases. Since the diameter is twice the radius, the diameter of the circle also increases. If the fish descends, then the diameter of the circle increases.
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