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 the three polarizers is $I$. The ratio $\left(\frac{I_0}{I}\right)$ equals (nearly) :

• A. $5.33$
• B. $16.00$
• C. $1.80$
• D. $10.67$

Answer 1

The correct option is D $10.67$

Let $I_1$ and $I_2$ are the intensities of light emerging from the polarizers $P_1$ and $P_2$, respectively.

So, $I_1=\frac{I_0}{2}$

$I_2=I_1{\cos }^2{\theta }_1$

And,$I=I_2{\cos }^2{\theta }_2$

Here, ${\theta }_1={30}^{\circ },\text{And}{\theta }_2={60}^{\circ }$

$\Rightarrow I=\left(\frac{I_0}{2}\right){\cos }^2{30}^{\circ }{\cos }^2{60}^{\circ }$

$I=\frac{I_0}{2}\times \frac{3}{4}\times \frac{1}{4}$

$\therefore \frac{I_0}{I}=\frac{32}{3}=10.67$.

Hence, $\left(C\right)$ is the correct answer.