A beam of unpolarised light of intensity $$I_0$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $$45°$$ relative to that of $$A$$. The intensity of emergent light is:

Unpolarised light of intensity $$I_0$$ passes through polaroid A, then polaroid B at $$45°$$.

After polaroid A (first polarizer), intensity becomes $$I_1 = \frac{I_0}{2}$$ (Malus's law for unpolarised light through a polarizer).

After polaroid B at angle $$45°$$ to A. By Malus's law: $$I_2 = I_1\cos^2 45° = \frac{I_0}{2} \times \frac{1}{2} = \frac{I_0}{4}$$.

The correct answer is Option 1: $$\frac{I_0}{4}$$.