Two ideal polaroids have mutually perpendicular transmission axes. A third ideal polaroid is inserted between them. At what angle relative to the first polaroid should the transmission axis of the middle polaroid be placed so that the final transmitted intensity is maximum?
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Question

Two ideal polaroids have mutually perpendicular transmission axes. A third ideal polaroid is inserted between them. At what angle relative to the first polaroid should the transmission axis of the middle polaroid be placed so that the final transmitted intensity is maximum?

Options

G1 Physics · Accepted Answer

Let the middle polaroid make angle θ with the first polarizer. Unpolarized incident light becomes I₁ = I₀ ÷ 2 after the first polarizer. After the middle polarizer, I₂ = (I₀ ÷ 2) cos²θ. The angle between the middle polarizer and the final crossed polarizer is 90°−θ. Thus, I₃ = (I₀ ÷ 2) cos²θ cos²(90°−θ) = (I₀ ÷ 2) cos²θ sin²θ. Using sin²2θ = 4sin²θ cos²θ, we get I₃ = I₀ ÷ 8 × sin²2θ. The intensity is maximum when sin²2θ = 1. Therefore, 2θ = 90°, so θ = 45°. Correct option: B.