The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at $22.5^{\circ}$ from the polarization axis of one of the polaroid, is ( $\mathrm{I}_0$ is the intensity of polarised light after passing through the first polaroid):

• A

  $\frac{\mathrm{I}_0}{2}$
• B

  $\frac{\mathrm{I}_0}{4}$
• Correct answer
  C

  $\frac{\mathrm{I}_0}{8}$
• D

  $\frac{\mathrm{I}_0}{16}$

Solution

Initially two polaroids are crossed i.e. $90^{\circ}$
After passing from first polaroid intensity is $\mathrm{I}_0$
$\begin{aligned} & \Rightarrow \frac{\mathrm{I}_0}{4} \sin ^2(2 \theta) \\ & \Rightarrow \frac{\mathrm{I}_0}{4} \sin ^2(2 \times 22.5) \\ & \Rightarrow \frac{\mathrm{I}_0}{8}\end{aligned}$

Hence, the correct answer is option: 'C'.