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Question

Unpolarized light of intensity 32 W m2 passes through three polarizers such that transmission axis of first is crossed with third. If the intensity of emerging light is 2 W m2, what is the angle between the transmission axes of the first two polarizers?

A
30
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B
60
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C
22.5
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D
45
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Solution

The correct option is C 22.5
The transmission axis of the first polarizer is crossed with the third.

Let θ be the angle between the axis of the first two polarizers then the angle between 2nd and 3rd polarizers will be (90θ).

Let I0 is the intensity of the unpolarized light incident on the first polarizer.
The intensity of light emerging from first polarizer is, I1=I02

According to Malu's law, The intensity of light emerging from second polarizer is,
I2=I02 cos2θ

And, The intensity of light emerging from third polarizer is,

I=(I02)cos2θcos2(90θ)

2=322cos2θcos2(90θ)

2=16cos2θsin2θ

12=4cos2θsin2θ

(2sinθcosθ)2=12

sin2 2θ=12

sin2θ=12

And, 2θ=45 θ=22.5

Hence, (C) is the correct answer.

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