A beam of unpolarised light with intensity I₀ falls on a system of three polaroids P₁ , P₂ , and P₃ arranged in series. The transmission axes of P₁ and P₃ are perpendicular to each other. If the transmission axis of P₂ is inclined at an angle of 15^ with respect to the transmission axis of P₁ , what will be the intensity of the light transmitted through P₃ ?

Step-by-step solution

Intensity of light after passing through P₁ is I₁ = I₀ 2 Angle between transmission axes of P₁ and P₂ is ₁ = 15^ Intensity of light after passing through P₂ is I₂ = I₁ ^2(15^ ) = I₀ 2 ^2(15^ ) Angle between transmission axes of P₁ and P₃ is 90^ Angle between transmission axes of P₂ and P₃ is ₂ = 90^ - 15^ = 75^ Intensity of light after passing through P₃ is I₃ = I₂ ^2(75^ ) = I₀ 2 ^2(15^ ) ^2(75^ ) Since (75^ ) = (15^ ) , we get: I₃ = I₀ 2 ( (15^ ) (15^ ))^2 I₃ = I₀ 2 ( (30^ ) 2 )^2 I₃ = I₀ 2 ( 1/2 2 )^2 = I₀ 2 ( 1