An unpolarised light beam of intensity 2 I _ 0 is passed through a...

When unpolarized light passes from Polaroid, then it becomes polarised light and intensity becomes half of the original, therefore, ${I}_{1} = \dfrac{2{I}_{0}}{2} = {I}_{0}$.

Given here, $\theta = 30 °$.

Using law of Malus for the second polariser, $I = {I}_{0}\cos^{2}\theta$

We have, intensity of emergent light, ${I}_{2} = {I}_{1}\cos^{2}30 °$

$= {I}_{0}\dfrac{3}{4} = \dfrac{3{I}_{0}}{4}$