Unpolarised light of intensity I₀ passes through two polaroids P₁ and P₂ whose pass axes are at an angle of 60^ to each other, yielding a transmitted intensity I₁ . A third polaroid P₃ is then inserted between them such that its pass axis bisects the angle between the pass axes of P₁ and P₂ , yielding a new final transmitted intensity I₂ . The ratio I₂ I₁ is :

Step-by-step solution

In the first configuration, unpolarised light of intensity I₀ passes through P₁ , so the intensity becomes I₀ 2 . The light then passes through P₂ , which is at an angle of 60^ relative to P₁ . By Malus's Law: I₁ = I₀ 2 ^2(60^ ) = I₀ 2 ( 1 2 )^2 = I₀ 8 In the second configuration, polaroid P₃ is inserted such that it bisects the angle between P₁ and P₂ . The angle between P₁ and P₃ is 30^ , and the angle between P₃ and P₂ is also 30^ . Intensity after P₁ is I₀ 2 . Intensity after P₃ is I₀ 2 ^2(30^ ) . Intensity aft