Question 173 of 191

An unpolarised light beam of intensity $2{I}_{0}$ is passed through a polaroid $P$ and then through another polaroid $Q$ which is oriented in such a way that its passing axis makes an angle of $30^{\circ}$ relative to that of $P$. The intensity of the emergent light is

A$\dfrac{{I}_{0}}{4}$B$\dfrac{{I}_{0}}{2}$C$\dfrac{3{I}_{0}}{4}$D$\dfrac{3{I}_{0}}{2}$

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Answer: (C) $\dfrac{3{I}_{0}}{4}$

When unpolarized light passes from Polaroid, then it becomes polarised light and intensity becomes half of the original, therefore, ${I}_{1}=\dfrac{2{I}_{0}}{2}={I}_{0}$.

Given here, $\theta =30^{\circ}$.
Using law of Malus for the second polariser, $I={I}_{0}{\cos }^{2}\theta$
We have, intensity of emergent light, ${I}_{2}={I}_{1}{\cos }^{2}30^{\circ}$
$={I}_{0}\dfrac{3}{4}=\dfrac{3{I}_{0}}{4}$