Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The angle between the polarizer A and C is $θ .$ Then

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$\cos θ = {(\frac{1}{3})}^{1 / 4}$

$\cos θ = {(\frac{1}{3})}^{1 / 2}$

$\cos θ = {(\frac{2}{3})}^{1 / 4}$

$\cos θ = {(\frac{2}{3})}^{1 / 2}$

answer is A.

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Detailed Solution

Case :I
Question Image
As light intensity does not change after passing through polarizer B Axis of B is parallel to axis of A
Case : II

By Malus law have
$I_{C} = \frac{I}{2} \cos^{2} θ$ and $I_{B} = I_{C} \cos^{2} θ = \frac{I}{2} \cos^{4} θ$
Given that $I_{B} = \frac{I}{3}$ $\Rightarrow \frac{I}{3} = \frac{I}{2} \cos^{4} θ$ $\Rightarrow \cos θ = {(\frac{2}{3})}^{1 / 4}$