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Chapter 11: Problem 18

A beam of unpolarized light is passed through two polarizers. If the polarization axis of the second polarizer is at an angle of \(90^{\circ}\) with respect to the axis of the first polarizer, then the intensity of light seen by someone located between them is (A) the intensity of the original light. (B) one-half the intensity of the original light. (C) one-quarter the intensity of the original light. (D) one-eighth the intensity of the original light. (E) zero.

Short Answer

Expert verified
Answer: (E) zero

Step by step solution

01

Unpolarized light intensity after passing through the first polarizer

The intensity of an unpolarized light is reduced to half when it passes through a polarizer. Let the intensity of the original light be \(I_0\). The intensity after passing through the first polarizer will then be: $$I_1 = \frac{1}{2} I_0$$
02

Intensity of light after passing through the second polarizer

After passing through the first polarizer, the light is now polarized. Next, the light passes through the second polarizer, which has a polarization axis at \(90^{\circ}\) with respect to the first polarizer. We will now use Malus's law to determine the intensity of the light after passing through the second polarizer: $$I_2 = I_1 \cdot \cos^2(90^{\circ})$$ We know that \(\cos(90^{\circ}) = 0\), so: $$I_2 = I_1 \cdot (0)^2 = 0$$
03

Final Intensity of light

After passing through both polarizers, the intensity of light seen by someone located between them is zero. So, the correct answer is: (E) zero.

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