MHTCET 23 Apr 2025 Shift 1 Paper

Concept:Malus’s law applied to two polaroids: first polaroid halves the intensity of unpolarised light, then the second polaroid transmits $\cos^2\theta$ of that intensity.Explanation:Let the incident unpolarised light intensity be $I_0$.After the first polaroid, the intensity becomes:$$I_1 = \frac{I_0}{2}$$The transmission axis of the second polaroid makes angle $\theta = 30^\circ$ with the first, so by Malus’s law:$$I_2 = I_1 \cos^2 30^\circ$$Substitute $I_1 = \frac{I_0}{2}$ and $\cos 30^\circ = \frac{\sqrt{3}}{2}$:$$I_2 = \frac{I_0}{2} \times \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{I_0}{2} \times \frac{3}{4} = \frac{3I_0}{8}$$Thus the fraction transmitted is:$$\frac{I_2}{I_0} = \frac{3}{8} = 0.375 = 37.5\%$$Answer:The fraction of incident unpolarised light transmitted is $37.5\%$, which corresponds to option D.