Question

part b and c

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: = 16 Inax (1 - Cos( 41 )) You will find the following trigonometric identities helpful: Cos”(@) = (1 + Cos(29) Sin”(@) = }(1-Cos(29)) Cos? (90° - 0) – Sin (0) b) Sketch a plot of the emerging intensity as a function of time using w = 0.5 rad, and Imax = 16 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

solution Z Given that I= Imad (1-cooluust) b 16 using Imad 16 w and w: 0.5 tond I. 16 16 (1-сoslu#0:5*2)) I - 1-60312_) : The function boils down to Il2)=1-coolat) The plot & Z Z qizce -2 1 -0.5 13 cape "Z ar To plot the function manually oo Sketching a couple of things. Sketching it note

Q The function is like l-carot or Every time the cos function has a value of 1 The intersily becomes a Whenever the cos Function becomes - The intensity becomco do shifting no This is Equivalent to the entire cog function up the y-axis such that there are Negalive values followzed by Stirling it to the eight by half a period (pi). such that the function becomes o al airr whese n=0.12, The period 2 | - Chat 2sing the wave is Eao Looking at this function, The period of Edacky 27. which is the exact same period as a regulat genusoidal warc. @ The function COOLUWE2

r=uw "2=40 in above Ean coo (unt) 200 (124) [.: 40=2 wave • Cosent) which looks like a cegulas sinusoichal 1 The of oscillation angulat frequency R=27 T #1a, 27 2 -in T 27 ar #lit J * 27 Loncoc Tis the time period. f r ar [.:F=] above r=uw Е. Иu9 21 F : 46 w 27 F=U* ar f the pocquency being which is u times the angular foequengy. poequency of of the disc having W = قا ar *

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