Physics - Wave Optics Question with Solution | TestHub

When unpolarised light of intensity $I_0$ passes through the first polaroid (sheet 1), the intensity of the emergent polarised light is:
$I_1=\frac{I_0}{2}$

The pass axis of sheet 2 makes an angle of $30^{\circ }$ with the pass axis of sheet 1. According to Malus's law, the intensity of light after passing through sheet 2 is:
$I_2=I_1{\cos }^2(30^{\circ })=\left(\frac{I_0}{2}\right){\left(\frac{\sqrt{3}}{2}\right)}^2=\frac{I_0}{2}\times \frac{3}{4}=\frac{3I_0}{8}$

The pass axis of sheet 3 makes an angle of $90^{\circ }$ with the pass axis of sheet 1. Therefore, the angle between the pass axes of sheet 2 and sheet 3 is:
$\theta =90^{\circ }-30^{\circ }=60^{\circ }$

Applying Malus's law again for sheet 3, the final emergent intensity is:
$I_3=I_2{\cos }^2(60^{\circ })=\left(\frac{3I_0}{8}\right){\left(\frac{1}{2}\right)}^2=\frac{3I_0}{8}\times \frac{1}{4}=\frac{3I_0}{32}$

Answer: $\frac{3{\mathrm{I}}_0}{32}$