Question

At which angle, the intensity of transmitted light is maximum when a polaroid sheet is rotated between two crossed polaroids?

• A. $\pi /4$
• B. $\pi /2$
• C. $\pi /3$
• D. $\pi$

Answer 1

The correct option is A $\pi /4$

Suppose $I_0$ be the intensity of polarized light after passing through the first polarizer $P_1$.

Then, the intensity of light emerging from the second polarizer will be,

$I=I_0{\cos }^2\theta$ [Malus's law]
where, $\theta$ is the angle between pass axes of $P_1\text{and}{P}_2$.

Since, the polaroids $P_1$ and $P_3$ are crossed, angle between pass axes of $P_2$ and $P_3$ will be $(\frac{\pi }{2}-\theta )$

Hence, the intensity of light emerging from $P_3$ will be,
$I=\left(I_0{\cos }^2\theta \right){\cos }^2(\frac{\pi }{2}-\theta )$
$=I_0{\cos }^2\theta .{\sin }^2\theta =\left(\frac{I_0}{4}\right){\sin }^{2}2\theta$

So, intensity will be maximum, when $\sin 2\theta =1$
$\Rightarrow 2\theta =\pi /2\text{or}\theta =\pi /4$

Therefore, the transmitted intensity will be maximum when $\theta =\pi /4.$

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

Why this question? To study and understand about situations involving multiple polarizers and apply Malu's law to them, individually.