An unpolarised light beam of intensity $$2I_0$$ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is

We have an unpolarised light beam of intensity $$2I_0$$ passing through polaroid P. When unpolarised light passes through a polaroid, its intensity is halved. So the intensity after P is $$\frac{2I_0}{2} = I_0$$.

Now this polarised light passes through polaroid Q, whose passing axis makes an angle of 30° with that of P. By Malus's law, the transmitted intensity is: $$I = I_0 \cos^2 30° = I_0 \left(\frac{\sqrt{3}}{2}\right)^2 = I_0 \cdot \frac{3}{4} = \frac{3I_0}{4}$$

Hence, the correct answer is Option 3.