Unpolarized light of intensity I_0 is made to pass through three...

Intensity of unpolarized light is $I_0$.

Intensity of light after passing through the first polarizer $P_1$ is:

$I_1 = \dfrac{I_0}{2}$

The polarization axis of $P_2$ makes an angle of 60^{}^{\circ} with $P_1$. According to Malus's law, the intensity after passing through $P_2$ is:

I_2 = I_1 \cos^2(60^{}^{\circ}) = \dfrac{I_0}{2} \times \left(\dfrac{1}{2}\right)^2 = \dfrac{I_0}{8}

The polarization axis of $P_3$ makes an angle of 45^{}^{\circ} with $P_2$. The intensity after passing through $P_3$ is:

I_3 = I_2 \cos^2(45^{}^{\circ}) = \dfrac{I_0}{8} \times \left(\dfrac{1}{\sqrt{2}}\right)^2 = \dfrac{I_0}{16}

Given $I_0 = x I_3$, substituting the value of $I_3$ gives:

$I_0 = x \left(\dfrac{I_0}{16}\right)<br><br>$x = 16$<br><br>Answer: 16$