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?

Answer 1

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`