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Chapter 29: Problem 26

Polarized light is incident on a sheet of polarizing material, and only \(20 \%\) of the light gets through. Find the angle between the electric field and the material's transmission axis.

Short Answer

Expert verified
The angle between the electric field and the material's transmission axis is approximately \( \theta = \cos^{-1}(\sqrt{0.2}) \), which calculates to about 63.4349 degrees.

Step by step solution

01

Understand Malus's Law

Malus's Law states that the intensity of light I after the polarizer is given by \( I = I_{0} \cos^2(\theta) \) where \( I_{0} \) is the original intensity of the light and \( \theta \) is the angle between the light's initial polarization direction and the polarizer's axis.
02

Set Up the Equation From Malus's Law

Given that only 20% of the light gets through the polarizer, we can write the equation from Malus's law as: \( 0.2 = \cos^2(\theta) \)
03

Solve for the Angle

Solving for \( \theta \) in the equation yields \( \theta = \cos^{-1}(\sqrt{0.2}) \)

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