An unpolarised light beam of intensity I₀ is incident on two polarising sheets placed one after another. If the angle between the transmission axes of the two sheets is 45^ , what is the intensity of the light emerging from the second sheet?

Step-by-step solution

When unpolarised light of intensity I₀ passes through the first polarising sheet, the transmitted light becomes linearly polarised and its intensity is halved: I₁ = I₀ 2 This linearly polarised light then passes through the second polarising sheet (analyser). According to Malus's law, the final transmitted intensity I₂ is: I₂ = I₁ ^2 Given the angle between the transmission axes is = 45^ : I₂ = ( I₀ 2 ) ^2(45^ ) I₂ = ( I₀ 2 ) ( 1 2 )^2 I₂ = ( I₀ 2 ) ( 1 2 ) = I₀ 4 Forgetting the initial halving of intensity for unp