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Find an Expression for Intensity of Transmitted Light When a Polaroid Sheet is Rotated Between Two Crossed Polaroids. - CBSE (Science) Class 12 - Physics

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Question

Find an expression for intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?

Solution

Let us consider two crossed polarisers P1 and P2, with a polaroid sheet P3 placed between them.

Let I0 be the intensity of polarised light after passing through the first polariser P1. If θ is the angle between the axes of P1 and P3, then the intensity of the polarised light after passing through P3 will be I=I0cos2θ.

As P1 and P2 are crossed, the angle between the axes of P1 and P2 = 90°.

∴ Angle between the axes of P2 and  P3 = (90°θ)

The intensity of light emerging from P2 will be given by

I=[I0cos2θ]cos2(90°θ)

I=[I0cos2θ]sin2θ

`=>I=I_0/4(4cos^2thetasin^2theta)`

`=>I=I_0/4(2sinthetacostheta^2)`

 `=>I=I_0/4sin^2theta`

 The intensity of polarised light transmitted from P2 will be maximum when

sin2θ=maximum=1

sin2θ=sin90°

2θ=90°

θ=45°

Also, the maximum transmitted intensity will be given by

`I=I_0/4`

  Is there an error in this question or solution?
Solution Find an Expression for Intensity of Transmitted Light When a Polaroid Sheet is Rotated Between Two Crossed Polaroids. Concept: Polarisation.
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