Question

Two polaroids P₁ and P₂ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity I₀ is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its pass axis makes an angle of 60° with that of P₁. Determine the intensity of light transmitted through P₁, P₂ and P₃.

A narrow beam of unpolarised light of intensity I₀ is incident on a polaroid P₁. The light transmitted by it is then incident on a second polariod P₂ with its pass axis making angle of 60° relative to the pass axis of P₁. Find the intensity of the light transmitted by P₂.

Answer 1

As given in the question the polaroid P₁ and P₂ are placed with their pass axes perpendicular to each other and polaroid P₃ placed at 60°with repect to P₁.

Therefore,
Intensity of light after falling on first polaroid  P_1, `I'=I_0/2`

Intensity of light after falling on third polaroid P₃

`I'' = I'cos^2(theta)=I_0/2cos^2(60^@)=I_0/8`

Therefore the intensity `I_0/8` will pass through the P₃ and angle between P3 and P2 is 30°. because of the condition given in the question.

Intensity of light after falling on second polaroid P₂ =

`I'''= I'' cos^2(theta)=I_0/8cos^2(30^@) = (3I_0)/32`