Question

Unpolarized light with intensity I₀ is incident on two polarizers initially oriented for maximum transmission. What is the intensity of the light transmitted through the second polarizer if the second polarizer is rotated through (a) 30° (b) 60°?

Answer 1

Data: θ = 30°, 60°

According to Malus’s law, when the unpolarized light with intensity I₀ is incident on the first polarizer, the intensity of the transmitted polarized light is I₁ = I₀/2. Subsequently, the intensity of the light transmitted by the second polarizer is

I₂ = I₁ cos²θ

∴ `I_2 = (I_0/2) cos^2θ`

(a) For θ = 30°: `I_2 = I_0/2cos^2 30°`

= `I_0/2 (sqrt3/2)^2`

= `3/8 I_0`

= 0.375 I₀

(b) For θ = 60°: `I_2 = I_0/2cos^2 60°`

= `I_0/2 (1/2)^2`

= `1/8 I_0`

= 0.125 I₀