Unpolarized light of intensity I₀ passes through a fixed polarizer and then through an analyser whose transmission axis is slowly and uniformly rotated from parallel to perpendicular relative to the first polarizer. What is the average transmitted intensity during this rotation?
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Question

Unpolarized light of intensity I₀ passes through a fixed polarizer and then through an analyser whose transmission axis is slowly and uniformly rotated from parallel to perpendicular relative to the first polarizer. What is the average transmitted intensity during this rotation?

Options

G1 Physics · Accepted Answer

After the first polarizer, I₁ = I₀ ÷ 2. At analyser angle θ, I(θ) = (I₀ ÷ 2) cos²θ. As θ varies uniformly from 0 to 90°, the average value of cos²θ over this interval is 1 ÷ 2. Therefore, I(avg) = (I₀ ÷ 2)(1 ÷ 2) = I₀ ÷ 4. Correct option: C.