A beam of light of intensity I₀ falls on a system of three polaroids which are arranged in succession such that the pass (transmission) axis is turned through 60^ with respect to preceding one. The fraction of the incident light intensity that passes through the system is ( 60^ =1 / 2 )

Step-by-step solution

For incident unpolarized light of intensity I₀ , passage through the first polaroid halves the intensity: I₁ = I₀ 2 , resulting in light polarized along the first axis. The second polaroid is rotated 60^ relative to the first. By Malus’s Law, the transmitted intensity is I₂ = I₁ ^2 60^ = I₀ 2 ( 1 2 )^2 = I₀ 8 . A third polaroid, rotated 60^ from the second, transmits I₃ = I₂ ^2 60^ = I₀ 8 1 4 = I₀ 32 . The fraction of incident intensity transmitted is I₃ I₀ = 1 32 . Final answer: B