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Chapter 31: Problem 51

A 10.0 -mW vertically polarized laser beam passes through a polarizer whose polarizing angle is \(30.0^{\circ}\) from the horizontal. What is the power of the laser beam when it emerges from the polarizer?

Short Answer

Expert verified
Answer: The power of the laser beam when it emerges from the polarizer is 7.50 mW.

Step by step solution

01

Understand Malus' Law

Malus' law states that the intensity of polarized light transmitted through a polarizer is reduced by a factor of the square of the cosine of the angle between the plane of polarization of the incident light and the polarizing axis of the polarizer. The equation is given as: \( I_{transmitted} = I_{incident} * \cos^{2}{\theta} \) Here, \(I_{transmitted}\) is the transmitted intensity of light, \(I_{incident}\) is the incident intensity of light, and \(\theta\) is the angle between the initial polarization plane and the polarizing axis of the polarizer.
02

Convert given power and angle units

The given power of the laser beam is 10.0 mW. We need to convert it to watts before plugging it into the equation. Also, the angle given is in degrees, and we need to have it in radians as \(\cos\) function takes radians. Power in watts: \( I_{incident} = 10.0 \cdot 10^{-3} W\) Convert angle from degrees to radians: \( \theta = 30 \cdot \frac{\pi}{180} \)
03

Apply Malus' Law and calculate transmitted power

Now we can apply Malus' law to find the transmitted power. \( I_{transmitted} = I_{incident} * \cos^{2}{\theta} \) \( I_{transmitted} = (10.0 \cdot 10^{-3}) * \cos^{2}\left(30 \cdot \frac{\pi}{180}\right) \)
04

Calculate final transmitted power

After evaluating the above expression, we have: \( I_{transmitted} = (10.0 \cdot 10^{-3}) * (0.866) ^{2} \) \( I_{transmitted} = 7.50 \cdot 10^{-3} W \) So, the power of the laser beam when it emerges from the polarizer is 7.50 mW.

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