Unpolarized light of intensity I₀ is incident on a system of three polaroids. The first and third polaroids are kept crossed. Match the angle of the middle polaroid relative to the first polaroid (List-I) with the final transmitted intensity (List-II). List-I List-II (A) 15^ (I) 0 (B) 30^ (II) I₀ 32 (C) 45^ (III) I₀ 8 (D) 90^ (IV) 3I₀ 32 Choose the correct answer from the options given below:

Step-by-step solution

When unpolarized light of intensity I₀ passes through the first polaroid, its intensity becomes I₁ = I₀ 2 . Let the angle of the middle polaroid with the first be . Since the third polaroid is crossed with the first, its angle with the middle polaroid is (90^ - ) . The final transmitted intensity is: I = I₁ ^2 ^2(90^ - ) I = I₀ 2 ^2 ^2 = I₀ 8 ^2(2 ) For (A) = 15^ : I = I₀ 8 ^2(30^ ) = I₀ 8 1 4 = I₀ 32 (Matches II) For (B) = 30^ : I = I₀ 8 ^2(60^ ) = I₀ 8 3 4 = 3I₀ 32 (Matches IV) For (C) = 45^ : I = I₀ 8 ^2(90^ ) =