An unpolarized light beam of intensity I₀ is incident on a system of three polarizers P₁ , P₂ , and P₃ . The transmission axes of P₁ and P₃ are crossed (perpendicular to each other). The final transmitted intensity through all three polarizers is found to be I₀ 32 . Assuming the angle between the transmission axes of P₁ and P₂ is an acute angle, its value is :

Step-by-step solution

Intensity of light after passing through P₁ is I₁ = I₀ 2 . Let the angle between P₁ and P₂ be . The intensity after P₂ is I₂ = I₁ ^2 = I₀ 2 ^2 . Since P₁ and P₃ are crossed, the angle between P₂ and P₃ is 90^ - . The intensity after P₃ is: I₃ = I₂ ^2(90^ - ) = ( I₀ 2 ^2 ) ^2 Using the identity 2 = (2 ) , we get: I₃ = I₀ 8 ^2(2 ) Given that I₃ = I₀ 32 , we have: I₀ 8 ^2(2 ) = I₀ 32 ^2(2 ) = 1 4 (2 ) = 1 2 (since is acute) 2 = 6 = 12 Answer: 12