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,
$I_2=I_{1}co{s}^2\left(90^{°}-\theta \right)=\frac{I_0}{2}co{s}^2\left(90^{°}-\theta \right)$
Also, $I_2=25\%$ of $I_0=\frac{I_0}{4}$
$\therefore \frac{I_0}{4}=\frac{I_0}{2}co{s}^2\left(90^{°}-\theta \right)$
$\Rightarrow co{s}^2\left(90^{°}-\theta \right)=\frac{1}{\sqrt{2}}=cos45^{°}$
or $\theta =90^{°}-45^{°}=45^{°}$