Question

A source of light is placed in front of a screen. Intensity of light on the screen is $I$. Two Polaroids $P_{1}and{P}_2$ are so placed in between the source of light and screen that the intensity of light on screen is $\frac{I}{2}$. $P_2$ should be rotated by an angle of ____(degrees) so that the intensity of light on the screen becomes $\frac{3I}{8}$.

• A. 30.0
• B. 30.00
• C. 30

Answer 1

Answer: (A), (B), (C)

The initial and final situations are shown below:



Let $\varphi$ be the angle by which the polaroid $P_2$ should be rotated.

By Malus law, we know that:

$I=\frac{I_0}{2}{\cos }^2\varphi$

According to the question,

$\frac{I}{2}{\cos }^2\varphi =\frac{3I}{8}$

$\Rightarrow {\cos }^2\varphi =\frac{3}{4}$

$\Rightarrow \cos \varphi =\frac{\sqrt{3}}{2}$

$\Rightarrow \varphi ={30}^{\circ }$