# Chapter 22 - Problems - Page 865: 50

(a) The transmitted intensity is $\frac{I_0}{8}$ (b) When the middle sheet is removed, the transmitted intensity is zero.

#### Work Step by Step

(a) Since the light is unpolarized initially, the intensity of the light after passing through the first polarizing sheet is $\frac{I_0}{2}$ We can use the law of Malus to determine the intensity of the light after passing through the second polarizing sheet. $I_2 = \frac{I_0}{2}~cos^2(45^{\circ}) = \frac{I_0}{4}$ We can determine the intensity of the light after passing through the third polarizing sheet. $I_3 = \frac{I_0}{4}~cos^2(45^{\circ}) = \frac{I_0}{8}$ The transmitted intensity is $\frac{I_0}{8}$ (b) Since the light is unpolarized initially, the intensity of the light after passing through the first polarizing sheet is $\frac{I_0}{2}$ We can use the law of Malus to determine the intensity of the light after passing through the second polarizing sheet. $I_2 = \frac{I_0}{2}~cos^2(90^{\circ}) = 0$ When the middle sheet is removed, the transmitted intensity is zero.

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