Two ideal polaroids are crossed. A third ideal polaroid is inserted between them with its transmission axis making an angle θ with the first polaroid. Unpolarized light of intensity I₀ is incident on the first polaroid. The final transmitted intensity is I₀ ÷ 16. What is the least positive value of θ?
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Question

Two ideal polaroids are crossed. A third ideal polaroid is inserted between them with its transmission axis making an angle θ with the first polaroid. Unpolarized light of intensity I₀ is incident on the first polaroid. The final transmitted intensity is I₀ ÷ 16. What is the least positive value of θ?

Options

G1 Physics · Accepted Answer

For crossed first and last polaroids with a middle polaroid at angle θ, I = (I₀ ÷ 2) cos²θ sin²θ = I₀ ÷ 8 × sin²2θ. Given, I = I₀ ÷ 16. Therefore, I₀ ÷ 8 × sin²2θ = I₀ ÷ 16. Thus, sin²2θ = 1 ÷ 2. The least positive value satisfying this condition is 2θ = 45°. Hence, θ = 22.5°. Correct option: B.