Question

Suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with and angular speed ω, this means θ = ωt.

a) Show that if unpolarized light is incident on the left disk with an intensity of Imax, the intensity of the beam emerging from the right disk is: I = 1 16 Imax (1 − Cos(4ωt)) You will find the following trigonometric identities helpful: Cos2 (θ) = 1 2 (1 + Cos(2θ)) Sin2 (θ) = 1 2 (1 − Cos(2θ)) Cos2 (90◦ − θ) = Sin2 (θ)

b) Sketch a plot of the emerging intensity as a function of time using ω = 0.5 rad s , and Imax = 16 W m2 .

c) Compare the frequency the disk rotates and the frequency of oscillation of you intensity plot. Explain how/why one is 4× the other.

Question 3: Consider the image below for the following problem statement. Suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with and angular speed w, this means 0 = wt. a) Show that if unpolarized light is incident on the left disk with an intensity of Imax, the intensity of the beam emerging from the right disk is: I Imax (1 – Cos(4wt)) 16 You will find the following trigonometric identities helpful: Cos? (0) = { (1 + Cos(20)) Sin?(0) = { (1 – Cos(20) Cos? (90° – 0) = Sin () b) Sketch a plot of the emerging intensity as a function of time using w= 0.5 rad, and Imax = 16 m. c) Compare the frequency the disk rotates and the frequency of oscillation of you intensity plot. Explain how/why one is 4x the other.

Answer 1

max Ans. O=wt &. Iz + stro >I, unpolasized light of inten- sity Imax is incident on polarizes? P. now. I = 2 Imax (since the incident light has electric field in att directions it making angle from oto an with the pass anis of f) malus' law giver I 2 = I costo f [max cos² (wt) 2 now the angle between the electric field and the pass anis of P₂ = E /2-wt 1/2-0

Q Again malus law gives I = I cos² (412- wt) Ź Imox Coswt) sin(wt) Imax 4 (1tcosew ta (9- Cos(2wt) Ś Imax (l-cosékwt).) Imax Sin?(2wt) now sin2wt) 1 - cos4 wt) Asin thence I = 1 Imax Imax (l- cosC4wt) 8 Y16 Imax (1-COSCHWE) = } sino = COS20 2 2 2

b) W: 0.5 lodla I max = 16 W/m² ² I=16 (1 - Cos (4x0.5t)) 16 I 1 - costat I 2 →t *12 30/2 A ho C) During one cotation of P there are four positions Where the electric field of light wo tao

niaka angle o with pass anis of la as shown in the figurei. wit itence the frequency of Oscillation of intensity piot ja 4 times the frequency the disk sotatea fi -P2 back to Twital position با د