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

Published by Pearson

# Chapter 31 - Electromagnetic Fields and Waves - Exercises and Problems - Page 903: 57

#### Answer

$\theta = 63.4^{\circ}$

#### Work Step by Step

When unpolarized light passes through a polarizing filter, the intensity of the transmitted light is $0.5~I_0$ where $I_0$ is the original intensity. Thus the intensity is $I_1 = 0.5~I_0$ after passing through the first filter. We can find the angle $\theta$ between the two filters: $I_2 = I_1~cos^2~\theta$ $0.1~I_0 = 0.5~I_0~cos^2~\theta$ $cos^2~\theta = 0.20$ $cos~\theta = \sqrt{0.20}$ $cos~\theta = 0.447$ $\theta = cos^{-1}~(0.447)$ $\theta = 63.4^{\circ}$

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