Question

$A$ system of three polarizers $P_1,P_2,P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$. The pass axis of $P_2$ is inclined at ${60}^{\circ }$ to the pass axis of $P_3$. When a beam of unpolarized light of intensity $I_0$ is incident on $P_1$ the intensity of light transmitted by three polarizers is $I$. The ratio $\left(\frac{I_0}{I}\right)$ equals (nearly)

• A. $\frac{16}{3}$
• B. $\frac{3}{32}$
• C. $\frac{32}{3}$
• D. $\frac{3}{16}$

Answer 1

The correct option is C $\frac{32}{3}$


Intensity of unpolarized light $=I_0$

Intensity of light transmitted from $P_1$ $I_1=\frac{I_0}{2}...\left(1\right)$

From Malus law that the intensity of light when passed through $P_2$,

$I_2=\frac{I_0}{2}(\cos {30}^{\circ }{)}^2....(2)$

Given that the intensity of light when passed through $P_3$ is $I$,

$I=I_2(\cos {60}^{\circ }{)}^2....(3)$

$\Rightarrow I=\frac{I_0}{2}\left(\cos {30}^{\circ }{)}^2\right(\cos {60}^{\circ }{)}^2\left(\text{from equation}\right(2\left)\right)$
$\Rightarrow I=\frac{I_0}{2}\times \frac{3}{4}\times \frac{1}{4}$

$\Rightarrow \frac{I_0}{I}=\frac{32}{3}$

Hence, option $\left(\text{C}\right)$ is correct.