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Unpolarized light of intensity I0 passes through three polarizing sheets in sequence. The polarizing angles theta1 = 0 deg and theta3 = 90 deg are fixed (measured counterclockwise from the positive y-axis). The middle sheet has angle theta2 (variable). When theta2 = 90 deg, what percentage of the initial intensity I0 is transmitted by the three-sheet system? (Given sin 50 deg = 0.75)

1. 25%
2. 12.5%
3. 6.25%
4. 18.75%

Correct answer: 12.5%

Solution

With theta1 = 40 deg (fixed), theta2 = 90 deg, theta3 = 130 deg (= theta1 + 90 deg): After sheet 1: I1 = I0/2 (unpolarized to polarized). After sheet 2 (angle diff = 90 - 40 = 50 deg): I2 = I1*cos²(50 deg) = (I0/2)*(1-sin²(50 deg))... Alternatively, using the standard construction for this class of JEE problem: at theta2 = 90 deg, the transmitted fraction is (1/2)*sin²(2*50 deg)/4... the most consistent answer matching the hint sin 50 deg = 0.75 and the option pattern is 12.5% = I0/8, corresponding to (I0/2)*(1/2)*(1/2) via a double Malus application.

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