Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 34 - Ray Optics - Exercises and Problems - Page 992: 47


(a) $\theta_1 = 2~cos^{-1}~(\frac{n}{2})$ (b) $\theta_1 = 82.8^{\circ}$

Work Step by Step

(a) We can use Snell's Law: $n_1~sin~\theta_1 = n_2~sin~\theta_2$ $(1)~sin~\theta_1 = n~sin~\frac{\theta_1}{2}$ $sin~(2\cdot \frac{\theta_1}{2}) = n~sin~\frac{\theta_1}{2}$ $2~sin~\frac{\theta_1}{2}~cos~\frac{\theta_1}{2} = n~sin~\frac{\theta_1}{2}$ $2~cos~\frac{\theta_1}{2} = n$ $cos~\frac{\theta_1}{2} = \frac{n}{2}$ $\frac{\theta_1}{2} = cos^{-1}~(\frac{n}{2})$ $\theta_1 = 2~cos^{-1}~(\frac{n}{2})$ (b) We can evaluate our expression for light incident on glass: $\theta_1 = 2~cos^{-1}~(\frac{n}{2})$ $\theta_1 = 2~cos^{-1}~(\frac{1.50}{2})$ $\theta_1 = (2)~(41.4^{\circ})$ $\theta_1 = 82.8^{\circ}$
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