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Question

Unpolarized light of intensity 32 Wm2 passes through three polarizers arranged in a way, such that the transmission axis of the last polarizer is crossed with that of the first. If the intensity of emerging light is 3 Wm2, what is the angle between the axis of first two polarizers?


A
45
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B
60
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C
30
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D
90
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Solution

The correct option is C 30

Now, angle between P1 and P3 is 90

Let,
θ1 angle between P1 & P2
And, θ2 angle between P2 & P3
θ1+θ2=90

After passing through 1st polarizer, the intensity becomes half, i.e. I1=I02

Now, intensity coming out of the 2nd polarizer is,
I2=I1 cos2θ1

Intensity coming out of the 3rd polarizer is,
I3=I2 cos2 θ1

Here, I3=3

I3=I1cos2θ1cos2θ2

3=16cos2θ1cos2(90θ1)

3=16cos2θ1sin2θ1

3=4×4cos2θ,sin2θ1

3=4(sin2θ1)2

sin22θ1=34

sin2θ1=32

2θ1=60

θ1=30

Hence, (C) is the correct angle.

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