Three polaroids P₁ , P₂ , and P₃ are arranged coaxially. The pass axes of P₁ and P₃ are perpendicular to each other. Unpolarised light of intensity I₀ is incident on P₁ . When P₂ is placed between P₁ and P₃ , the final transmitted intensity of light is found to be I₀ 32 . The minimum positive angle between the pass axes of P₁ and P₂ is :

Step-by-step solution

The intensity of unpolarised light after passing through the first polaroid P₁ becomes half. Intensity after P₁ , I₁ = I₀ 2 Let the angle between the pass axes of P₁ and P₂ be . According to Malus's Law, the intensity after P₂ is: I₂ = I₁ ^2 = I₀ 2 ^2 Since the pass axes of P₁ and P₃ are perpendicular, the angle between the pass axes of P₂ and P₃ is (90^ - ) . The intensity after P₃ is: I₃ = I₂ ^2(90^ - ) = ( I₀ 2 ^2 ) ^2 Using the identity 2 = (2 ) , this can be written as: I₃ = I₀ 8 ^2(2 ) It is given that the fi