A beam of unpolarized light of intensity I₀ passes through a sequence of three polarizers. The first and third polarizers are fixed with their transmission axes perpendicular to each other. The middle polarizer rotates about the axis of the light beam with a constant angular velocity . At time t=0 , the transmission axis of the middle polarizer is parallel to that of the first polarizer. The ratio of the maximum tran

Step-by-step solution

The intensity of light after the first polarizer is I₁ = I₀ 2 . At time t , the angle of the middle polarizer with respect to the first is = t . The intensity after the middle polarizer is I₂ = I₁ ^2( t) = I₀ 2 ^2( t) . The third polarizer is perpendicular to the first, so the angle between the middle and third polarizers is 90^ - t . The final transmitted intensity is: I(t) = I₂ ^2(90^ - t) = I₀ 2 ^2( t) ^2( t) Using the double angle formula, I(t) = I₀ 8 ^2(2 t) . The maximum transmitted intensity occurs when ^2(2