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Unpolarized light of intensity $32 {Wm}^{- 2}$ passes through three polarizer’s such that the transmission axis of the last polarizer is crossed with that of the first. The intensity of final emerging light is $3 {Wm}^{- 2}$ .The intensity of light transmitted by second polarizer will be

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answer is 12.

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Detailed Solution

$I_{1} = \frac{I_{0}}{2};$

$I_{2} = \frac{I_{0}}{2} \cos^{2} (θ);$

$I_{3} = \frac{I_{0}}{2} \cos^{2} (θ) \cos^{2} (90 ° - θ) = \frac{I_{0}}{8} \sin^{2} (2 θ)$

$\Rightarrow 3 = \frac{32}{8} \sin^{2} (2 θ) \Rightarrow θ = 30 °$

$\Rightarrow I_{2} = \frac{I_{0}}{2} \cos^{2} (θ) = 12 {Wm}^{- 2}$

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