Unpolarized light of intensity I₀ is incident on a pair of crossed polaroids. A third polaroid is placed between them and is made to rotate at a constant angular velocity about the axis of the light beam. The angular frequency of the fluctuations in the intensity of the transmitted light is:

Step-by-step solution

Let the initial unpolarized light intensity be I₀ . After passing through the first polaroid, the intensity becomes I₁ = I₀ 2 and the light is plane-polarized. Let the rotating middle polaroid be at an angle = t with respect to the first polaroid at time t . The intensity after the middle polaroid is: I₂ = I₁ ^2( t) = I₀ 2 ^2( t) Since the first and third polaroids are crossed, the angle between the middle and third polaroids is (90^ - t) . The final transmitted intensity is: I₃ = I₂ ^2(90^ - t) = I₀ 2 ^2( t) ^2( t