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

Answer: (A)

Suppose $I_0$ be the intensity of polarised light after passing through the first polariser $P_1$. Then, the intensity of light after passing through second polariser will be
$I=I_0{\cos }^2\theta$
where, $\theta$ is the angle between pass axes of $P_1$ and $P_2$. Since, $P_1$ and $P_3$ are crossed the angle between the pass axes of $P_2$ and $P_3$ will be $\left(\frac{\pi }{2}-\theta \right)$.
Hence, the intensity of light emerging from $P_3$ will be
$I=I_0{\cos }^2\theta {\cos }^2\left(\frac{\pi }{2}-\theta \right)$
$=I_0{\cos }^2\theta \cdot {\sin }^2\theta =\left(\frac{I_0}{4}\right){\sin }^{2}2\theta$
Therefore, the transmitted intensity will be maximum when $\theta =\pi /4$.