Unpolarized light of intensity I₀ is incident on a system of three polaroids. The transmission axes of the first and third polaroids are crossed. If the final transmitted intensity of light is I₀ 32 , what is the angle between the transmission axes of the first and second polaroids?

Step-by-step solution

Intensity of light after passing through the first polaroid is I₁ = I₀ 2 . Let the angle between the transmission axes of the first and second polaroids be . The intensity after the second polaroid is I₂ = I₁ ^2 . Since the first and third polaroids are crossed, the angle between the second and third polaroids is (90^ - ) . The final intensity after the third polaroid is: I₃ = I₂ ^2(90^ - ) = I₁ ^2 ^2 Using the identity = (2 ) 2 , we get: I₃ = I₁ 4 ^2(2 ) = I₀ 8 ^2(2 ) Given that I₃ = I₀ 32 , we have: I₀ 8 ^2(2 ) =