Three identical polaroids P₁, P₂ and P₃ are placed one after another. The pass axis of P₂ and P₃ are inclined at an angle of 60^ and 90^ with respect to axis of P₁ . The source has an intensity 256 ~W / m ^2 . The intensity of light at point ' O ' is ( 30^ = 3 / 2, 60^ =0 5 )

Step-by-step solution

Given unpolarized initial intensity I₀ = 256 ~W / m ^2 . After passing through the first polarizer P₁ at 0^ , the intensity reduces by half: I₁ = I₀ 2 = 128 ~W / m ^2 . Light emerging from P₁ is polarized at 0^ and encounters P₂ at 60^ . By Malus's law, I₂ = I₁ ^2(60^ ) = 128 (0.5)^2 = 32 ~W / m ^2 . The polarization direction is now aligned with P₂ 's axis at 60^ . Transmission through P₃ at 90^ gives the final intensity: I₃ = I₂ ^2(30^ ) = 32 ( 3 2 )^2 = 32 3 4 = 24 ~W / m ^2 . The intensity at point O is 24 ~W /