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Chapter 29: Problem 42

Unpolarized light of intensity \(S_{0}\) passes first through a polarizer with its axis vertical and then through one with its axis at \(35^{\circ}\) to the vertical. Find the intensity after the second polarizer.

Short Answer

Expert verified
The intensity of the light after the second polarizer can be calculated by using Malus's law, which results in \( S = (S_{0} / 2) \cdot \cos^{2} (35^{\circ}) \).

Step by step solution

01

Apply Malus's Law

According to Malus's law, the intensity of the light after the second polarizer, denoted as \( S \), is given by the product of the intensity of the light after the first polarizer, i.e., half of the initial intensity \( S_{0} / 2 \), and the square of the cosine of the angle between the axes of the first and second polarizer. Hence, the formula is \( S = (S_{0} / 2) \cdot \cos^{2} (35^{\circ}) \).
02

Calculate Cosine Squared

To proceed with the calculations, calculate the value of \( \cos^{2} (35^{\circ}) \). Use a calculator to determine the cosine of the given angle, then square the result.
03

Calculate Intensity After Second Polarizer

Now, substitute the value of \( \cos^{2} (35^{\circ}) \) into the formula derived in step 1 to calculate the intensity of the light after the second polarizer.

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