Question

When a Polaroid sheet is rotated between two crossed polaroids, the intensity of the transmitted will be maximum, when angle $\theta$ between pass axes is

• A. $\frac{\pi }{2}$
• B. $\frac{3\pi }{4}$
• C. $\frac{\pi }{4}$
• D. $\frac{2\pi }{3}$

Answer 1

Answer: (C)

Let $I_0$ be the intensity of polarized light after passing through the first polarizer $P_1.$ Then the intensity of light after passing through second polarizer $P_2$ will be
$L=I_{0}co{s}^{2}q$
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 $P_2$ will be
$I=I_0{\left(cos\right)}^2\theta {\left(cos\right)}^2\left(\frac{\pi }{2}-\theta \right)$
$I=I_0{\left(cos\right)}^2\theta {\left(sin\right)}^2\theta =\left(\frac{I_0}{4}\right){\left(sin\right)}^2$
$2\theta$
Hence, transmitted intensity will be maximum,
when $\theta =\frac{\pi }{4}.$