An unpolarized light beam of intensity I₀ passes through a series of n Polaroids P₁, P₂, P₃, P_n . The pass axis of each poloroid makes an angle of 60^ with the other poloroid. What is the final intensity of the transmitted beam? ( 60^ = 1/2)

Step-by-step solution

Initial intensity of the unpolarized light is I₀ . When unpolarized light passes through the first polaroid P₁ , the intensity becomes half. Thus, the intensity after P₁ is: I₁ = I₀ 2 For each subsequent polaroid P_k ( k = 2, 3, , n ), the angle between its pass axis and the plane of polarization of the incident light is 60^ . According to Malus's Law, the intensity after passing through the k -th polaroid is: I_k = I_ k-1 ^2(60^ ) Since (60^ ) = 1 2 , we get: I_k = I_ k-1 ( 1 2 )^2 = I_ k-1 4 Applying this relatio