Unpolarised light of intensity $32 {Wm}^{- 2}$ passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is $3 {Wm}^{- 2}$ , then the angle between pass axis of first two polaroids is --------- (in degree).

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answer is 30.

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Detailed Solution

$I_{0} = 32; I_{1} = \frac{I_{0}}{2} = 16; I_{2} = I_{1} \cos^{2} θ$

$I_{3} = I_{2} \cos^{2} (90 - θ); I_{3} = I_{1} \cos^{2} θ \sin^{2} θ$

$\Rightarrow (sinθcosθ) = \frac{\sqrt{3}}{2} \Rightarrow \sin 2 θ = \frac{\sqrt{3}}{2}$

$\Rightarrow θ = 30^{0} .$

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