6a [25] In the lab you observe light from two unpolarized sources of intensity I₁ and I₂ passing through two polarizers, a and b, arranged in sequence as shown. The polarization or transmission directions are indicated by e_a and e_b, respectively. The axis e_a and e_b are at an angle q with respect to each other.

Show all work and explain relevant assumptions!

I₁, I₂ (a) (b)

i[8] What is the intensity of each beam (I_1a,I_2a) after passing through the first polarizer? Explain your answer!

I_1a = I₁/2 and I_2a = I₂/2 because unpolarized light has the E vector at all angles between 0 – 2p.

When we average cos²q from 0 – 2p we obtain the ½.

ii[17] When q = 30° you observe that the emergent light through both a and b from source 1, I_1f, has the same intensity as the emergent light from source 2, I_2f, when q = 60°. What is the relative intensity (I₁/I₂) of the two sources? Show all work and explain relevant assumptions!

I_1f = (1/2)I₁cos²30° = (1/2)I₂cos²60° ==>

I_1f/ I_2f = cos²60°/ cos²30° = (1/4)/(3/4) = 1/3