Optics - Polarization

Unpolarized light of intensity I₀ is incident on a series of three polarizing filters. The axis of the second filter is oriented at 45^o to that of the first filter, while the axis of the third filter is oriented at 90^o to that of the first filter. What is the intensity of the light transmitted through the third filter?

A. 0
B. I₀/8
C. I₀/4
D. I₀/2
E. I₀/√2

(GR0177 #51)

Solution:

Polarizer:
The first filter always reduces the intensity of the light to half, I₁=½ I₀
The next filter reduces the intensity by I_n = I_(n-1) cos² θ
θ is the angle with respect to the n^th filter.

Thus,

I₁ = ½ I₀

I₂ = I₁ (cos 45)² = I₁ (½ √2)² = ½ I₁ = ¼ I₀

I₃=I₂ (cos 45)² = ½ I₂ = I₀/8

Answer: B