## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 22 - Problems - Page 865: 47

#### Answer

21% of the initial light intensity is transmitted through this set of polarizers.

#### Work Step by Step

Let $I_0$ be the intensity of the incident light. Since the light is unpolarized initially, the intensity of the light after passing through the first polarizer is $\frac{I_0}{2}$ We can use the law of Malus to determine the intensity of the light after passing through the second polarizer. $I_2 = \frac{I_0}{2}~cos^2(30.0^{\circ}) = \frac{3~I_0}{8}$ We can determine the intensity of the light after passing through the third polarizer. $I_3 = \frac{3~I_0}{8}~cos^2(60.0^{\circ}-30.0^{\circ}) = \frac{9~I_0}{32}$ We can determine the intensity of the light after passing through the fourth polarizer. $I_4 = \frac{9~I_0}{32}~cos^2(90.0^{\circ}-60.0^{\circ}) = \frac{27~I_0}{128} = 0.21~I_0$ 21% of the initial light intensity is transmitted through this set of polarizers.

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