Q: Discuss the intensity of transmitted light when a Polaroid sheet is rotated between two crossed polaroids ?

Sol: let I_0 be the intensity of polarised light after passing through the first polariser P_{1} . Then the intensity P_{2} will be

I = I_{2} cos^{2} θ, Where θ is the angle between pass axes of P_{1} and P_{2} .

Since P_{1} and P_{2} are crossed the angle between the pass axes of P_{2} and P_{3} will be (π/2- θ). Hence the intensity of light emerging from P_{3} will be

I = I_{0} cos^{2} θ cos^{2} (π/2-θ)

= I_{0} cos^{2} θ sin^{2} θ = (I_{0}/4) sin^{2} 2 θ

Therefore, the transmitted intensity will be maximum when 𝜃 = π⁄4.