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Question

# Unpolarized light of intensity 32 W/m2 passes through three polarizers such that the transmission axis of the last polarizer is crossed with the first. If the intensity of emerging light is 3 W/m2, the angle θ between the transmission axes of the first two polarizers and the angle ϕ at which transmitted intensity will be maximum are

A
θ=30, ϕ=60
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B
θ=45, ϕ=45
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C
θ=30, ϕ=45
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D
θ=45, ϕ=30
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Solution

## The correct option is C θ=30∘, ϕ=45∘ Given: Intensity of unpolarized lightI0=32 W/m2 The intensity of light after passing through P3, I=I02 cos2θ sin2θ But it is given that I=3 W/m2 ⇒3=322cos2θsin2θ ⇒3=4×4cos2θsin2θ ⇒34=(2 sinθ cosθ)2 ⇒(sin2θ)2=34 ⇒sin2θ=√32=sin60∘ ⇒2θ=60∘ ∴θ=30∘ Also, I will be maximum when dIdθ=0 ⇒ddθ{I0×42×4cos2θsin2θ}=0 ⇒I08ddθ{sin22θ}=0 ∴2sin2θcos2θ×2=0 ⇒sin4θ=0 ⇒4θ=0∘, 180∘... ∴θmax=45∘ Angle at which intensity is maximumϕ=θmax=45∘ Hence, option (C) is correct.

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