Question

In: Physics

In the figure, unpolarized light is sent into a system of three polarizing sheets, which transmits...

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?

Solutions

Expert Solution

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 sin22

                              I3 /Io = (1/8) sin22

given that I3 /Io =0.0695

              (1/8)sin22   = 0.0695

                    sin22    = 0.556

                     sin2θ2   =0.746

     Answer (a)    smaller angle = θ2 = 24.12o          

Answer (b)    larger angle =90o2 = 65.88o


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