Three polarizing filters are stacked with the polarizing axes of the second and third at 45.0∘ and 90.0∘, respectively, with that of the first. (a) If unpolarized light of intensity I0 is incident on the stack, find the intensity and state of polarization of light emerging from each filter. (b) If the second filter is removed, what is the intensity of the light emerging from each remaining filter?

a) the intensity of the polarization of light emerging from each filter is I₀/2, 0.25 I₀ and 0.125 I₀

b) the intensity of light emerging from the each remaining filter is I₀ / 2 and 0.

Explanation:

a) The intensity of the incident light is I₀ and therefore the intensity of light transmitted through the first filter is

I₁ = I₀ / 2

The polarizing direction will be parallel to the axis of the first filter intensity of light transmitted through the second filter:

I₂ = I₁ cos² (θ₁)

I₂ = (I₀ / 2) cos² (45°)

I₂ = 0.25 I₀

Therefore, the polarizing direction will be at 45° to the axis of the first filter. The light intensity transmitted through the filter will be

I₃ = I₂ cos² (θ₂ - θ₁)

I₃ = I₂ cos² (90 - 45)

I₃ = I₂ cos² (45)

I₃ = 0.25 I₀ cos² (45)

I₃ = 0.125 I₀

Therefore, the intensity of the polarization of light emerging from each filter is I₀/2, 0.25 I₀ and 0.125 I₀

b) the intensity of light transmitted through the first filter is

I₁ = I₀ / 2

when the second filter is removed.

The intensity of light that is transmitted through the third filter is:

I₃' = I₁ cos² (90)

I₃' = (I₀ / 2) (0)

I₃' = 0

Therefore, the intensity of light emerging from the each remaining filter is I₀ / 2 and 0.