Polarization

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GRE Subject Test: Physics › Polarization

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1

A beam of unpolarized light passes through two linear polarizers whose polarization axes are at an angle theta with each other. The light initially has an intensity , and has an intensity of $\frac{3}{8}I_o$ after passing through both polarizes. Find $\theta$ ?

$30^\circ$

$60^\circ$

$45^\circ$

$90^\circ$

$180^\circ$

Explanation

Initially unpolarized light passing though a linear polarizer decreases in intensity by a factor of two:

$I=\frac{I_o}{2}$

Malus's Law gives the change in intensity of polarized light passing through a linear polarizer in terms of the change in angle of polarization:

$I=I_o\cos^2\theta$

Combining the two equations, we get:

$I=\frac{I_o}{2}\cos^2\theta$

Solving for $\theta$ :

$\theta=\cos^{-1}(\sqrt{\frac{2I}{I_o}})=\cos^{-1}(\sqrt{\frac{2\frac{3I_o}{8}}{I_o}})=\cos^{-1}(\frac{\sqrt{3}}{2}) =30^\circ$

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