Question

A beam of unpolarised light is incident on two polaroids crossed to each other. When one of the polaroid is rotated through an angle, then 25% of the incident unpolarised light is transmitted by the polaroids. Then the angle through which polaroid is rotated, is

• A. $25^°$
• B. $45^°$
• C. $0^°$
• D. $90^°$

Answer 1

Answer: (B)

Let $I_0$ be intensity of incident light, then the intensity of light emerging from the first polaroid,
$I_{1}=\frac{I_{0}}{2}$
Initially, the two polaroids are crossed to each other i.e. $ \theta_{i}= 90^{°}$
Let the polaroid be rotated by angle \theta, then the angle between polarising directions is $90^{°}-\theta$
Now, intensity of light emerging from the second polaroid,
$I_{2}=I_{1}\,cos^{2}\left(90^{°}-\theta\right)=\frac{I_{0}}{2} cos^{2}\left(90^{°}-\theta\right)$
Also, $I_{2}=25\%$ of $I_{0}=\frac{I_{0}}{4}$
$\therefore \frac{I_{0}}{4}=\frac{I_{0}}{2}cos^{2}\left(90^{°}-\theta\right)$
$\Rightarrow cos^{2}\left(90^{°}-\theta\right)=\frac{1}{\sqrt{2}}=cos\,45^{°}$
or $\theta=90^{°}-45^{°}=45^{°}$