MHTCET 22 Apr 2025 Shift 2 Paper

Concept:Malus’ law governs intensity after each polaroid: $I = I_0 \cos^2 \phi$.Explanation:Since no light emerges from the second polaroid, its axis is perpendicular to the first polaroid’s axis.So the angle between polaroid 1 and polaroid 2 is $90^\circ$.When a third polaroid is placed between them at angle $\theta$ to the first polaroid, the angle between polaroid 3 and polaroid 2 becomes $90^\circ - \theta$.After passing through the first polaroid, the intensity is:$$I_1 = \frac{I_0}{2}$$After passing through the third polaroid, by Malus’ law:$$I_2 = I_1 \cos^2 \theta = \frac{I_0}{2} \cos^2 \theta$$After passing through the second polaroid, the angle is $90^\circ - \theta$, so:$$I_3 = I_2 \cos^2(90^\circ - \theta) = \frac{I_0}{2} \cos^2 \theta \sin^2 \theta$$Simplify using $2\sin\theta\cos\theta = \sin 2\theta$:$$I_3 = \frac{I_0}{8}(\sin 2\theta)^2$$Answer:$$I_3 = \frac{I_0}{8}(\sin 2\theta)^2$$Correct option: B.