A clear sheet of Polaroid is placed on top of a similar sheet so that their axes make an angle of sin - 1 4 5 with each other. The ratio of the intensity of the emergent light to that of polarised light is

Step-by-step solution

Given, angle between polariser and analyser, θ = sin - 1 4 5 ⇒ sinθ = 4 5 ∴ cosθ = 1 - sin 2 θ = 3 5 Intensity of transmitted light is given by law of Malus, I = I 0 cos 2 θ where I and I 0 are the intensities of the polarised and emergent light respectively. ∴ I I 0 = cos 2 θ ⇒ I I 0 = 3 5 2 ⇒ I I 0 = 9 25 Hence, the required ratio is 9 : 25 .