Three polaroids P₁ , P₂ , and P₃ are placed coaxially. The pass axes of P₁ and P₃ are crossed (at 90^ to each other). An unpolarized light beam of intensity I₀ is incident on P₁ . The polaroid P₂ is placed between P₁ and P₃ . If the intensity of the light emerging from P₃ is I₀ 32 , what is the angle between the pass axes of P₁ and P₂ ?

Step-by-step solution

The intensity of unpolarized light after passing through the first polaroid P₁ becomes half: 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 P₁ and P₃ are crossed, the angle between their pass axes is 90^ . Thus, the angle between the pass axes of P₂ and P₃ is (90^ - ) . The intensity emerging from P₃ is: I₃ = I₂ ^2(90^ - ) = ( I₀ 2 ^2 ) ^2 Using the trigonometric identity 2 = (2 ) , we can rewrite this as: I₃ = I₀ 8 (2