Physics - Wave Optics Question with Solution | TestHub

Let the initial intensity of the unpolarized light from the source be $I_0=256{W/m}^2$.

When this unpolarized light passes through the first polaroid $P_1$, it becomes linearly polarized. The intensity of the transmitted light is half of the initial intensity:
$I_1=\frac{I_0}{2}=\frac{256}{2}=128{W/m}^2$

The pass axis of the second polaroid $P_2$ is inclined at an angle ${\theta }_1=60^{\circ }$ with respect to $P_1$. According to Malus's Law, the intensity of light after passing through $P_2$ is:
$I_2=I_1{\cos }^2(60^{\circ })$
$I_2=128\times {\left(\frac{1}{2}\right)}^2=128\times \frac{1}{4}=32{W/m}^2$

The pass axis of the third polaroid $P_3$ is inclined at an angle of $90^{\circ }$ with respect to $P_1$. Therefore, the angle between the pass axes of $P_2$ and $P_3$ is:
${\theta }_2=90^{\circ }-60^{\circ }=30^{\circ }$

Applying Malus's Law again, the intensity of light at point 'O' after passing through $P_3$ is:
$I_3=I_2{\cos }^2(30^{\circ })$
$I_3=32\times {\left(\frac{\sqrt{3}}{2}\right)}^2=32\times \frac{3}{4}=24{W/m}^2$

Answer: $24\mathrm{W}/{\mathrm{m}}^2$