Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the transmitted light is one third of intensity of the incident beam ?

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$\cos^{- 1} \sqrt{\frac{2}{5}}$

$\cos^{- 1} \sqrt{\frac{5}{2}}$

$\cos^{- 1} \sqrt{\frac{3}{2}}$

$\cos^{- 1} \sqrt{\frac{2}{3}}$

answer is D.

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Detailed Solution

Intensity of the light transmitted through first polarizer $I_{1} = \frac{I_{0}}{2}$

$I_{0} =$ Intensity of the incident unpolarized light, Intensity of the light transmitted through the second polarizer is $I_{2} = I_{1} \cos^{2} θ$

$I_{2} = I_{1} \cos^{2} θ = \frac{I_{0}}{2} \cos^{2} θ = \frac{I_{0}}{3}$

$\cos θ = \sqrt{\frac{2}{3}}$

$θ = \cos^{- 1} \sqrt{\frac{2}{3}}$

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