Question

Unpolarized light with intensity I0 is incident on two polaroids. The axis of the first polaroid makes an angle of 50 with the vertical, and the axis of the second polaroid is horizontal. What is the intensity of the light after it has passed through the second polaroid?

Answer 1

According to Malus’ law, when the unpolarized light with intensity I₀ is incident on the first polarizer, the polarizer polarizes this incident light. The intensity of light becomes I₁ = I₀/2.

Now, I₂ = I₁ cos²θ

I₂ = \((\frac{I_0}{2})\) cos²θ

Also, the angle θ between the axes of the two polarizers is θ₂ — θ₁.

∴ I₂ = \((\frac{I_0}{2})\)cos²(θ₂ — θ₁)

= \((\frac{I_0}{2})\)cos²(90° — 50°)

I₂ = \((\frac{I_0}{2})\)cos²40°

The intensity of light after it has passed through the second polaroid = \((\frac{I_0}{2})\)cos²40° = \((\frac{I_0}{2})\)(0.7660)²

= 0.2934 I₀