Physics - Wave Optics Question with Solution | TestHub

Intensity of unpolarised light incident on the first polaroid is ${\mathrm{I}}_0$.

Intensity of light transmitted through the first polaroid is:
$I_1=\frac{{\mathrm{I}}_0}{2}$

According to Malus's law, the intensity of light transmitted through the second polaroid is:
$I_2=I_1{\cos }^2\theta$
Given $\theta =30^{\circ }$, we get:
$I_2=\frac{{\mathrm{I}}_0}{2}{\cos }^2(30^{\circ })=\frac{{\mathrm{I}}_0}{2}{\left(\frac{\sqrt{3}}{2}\right)}^2=\frac{{\mathrm{I}}_0}{2}\times \frac{3}{4}=\frac{3{\mathrm{I}}_0}{8}$

Intensity of light transmitted through the third polaroid is:
$I_3=I_2{\cos }^2(30^{\circ })=\frac{3{\mathrm{I}}_0}{8}{\left(\frac{\sqrt{3}}{2}\right)}^2=\frac{3{\mathrm{I}}_0}{8}\times \frac{3}{4}=\frac{9{\mathrm{I}}_0}{32}$

Intensity of light transmitted through the fourth polaroid is:
$I_4=I_3{\cos }^2(30^{\circ })=\frac{9{\mathrm{I}}_0}{32}{\left(\frac{\sqrt{3}}{2}\right)}^2=\frac{9{\mathrm{I}}_0}{32}\times \frac{3}{4}=\frac{27{\mathrm{I}}_0}{128}$

Answer: $\frac{27{\mathrm{I}}_0}{128}$