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An unpolarised light of intensity $I$ is passed through two polaroids kept one after the other with their planes parallel to each other. The intensity of light emerging from second polaroid is $\frac{I}{4}$. The angle between the pass axes of the polaroids is
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The correct answer is:
$45^{\circ}$
The given situation is shown in the figure.
According to law of Malus,
$\begin{aligned} I^{\prime} & =\left(\frac{I}{2}\right) \cos ^2 \theta \\ \Rightarrow \quad \frac{I}{4} & =\frac{I}{2} \cos ^2 \theta \\ \Rightarrow \cos ^2 \theta & =\frac{1}{2} \\ \Rightarrow \cos \theta & =\frac{1}{\sqrt{2}} \\ \Rightarrow \quad \theta & =45^{\circ}\end{aligned}$
According to law of Malus,
$\begin{aligned} I^{\prime} & =\left(\frac{I}{2}\right) \cos ^2 \theta \\ \Rightarrow \quad \frac{I}{4} & =\frac{I}{2} \cos ^2 \theta \\ \Rightarrow \cos ^2 \theta & =\frac{1}{2} \\ \Rightarrow \cos \theta & =\frac{1}{\sqrt{2}} \\ \Rightarrow \quad \theta & =45^{\circ}\end{aligned}$
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