In: Physics
In the figure, unpolarized light is sent into a system of three polarizing sheets, which transmits 0.0695 of the initial light intensity. The polarizing directions of the first and third sheets are at angles θ1 = 0o and θ3 = 90o. What are the (a) smaller and (b) larger possible values of angle θ2 (< 90o) for the polarizing direction of sheet 2?
In Polarizer when the light is passed through the first polarizing Sheet then its transmitted intensity becomes half
or I= (1/2) Io
Now, This light is passed through the second Sheet then
I2 = I1 cos2θ2
=(1/2)Io cos2θ2
Finally this light is Passed through the third Sheet
I3= I2cos2(90-θ2)
= I1cos2θ2cos2(90-θ2)
= (1/2)Io cos2θ2sin2θ2
= (1/8) Io ( 2sinθ2cosθ2)2
= (1/8) Io sin2 2θ2
I3 /Io = (1/8) sin22θ2
given that I3 /Io =0.0695
(1/8)sin2 2θ2 = 0.0695
sin2 2θ2 = 0.556
sin2θ2 =0.746
Answer (a) smaller angle = θ2 = 24.12o
Answer (b) larger angle =90o-θ2 = 65.88o