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Light travelling through several polarizers

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data
    This is problem 71, chapter 38 in Physics for Scientists and Engineers 8th edition by Serway/Jewett.

    Three polarizers are situated in a straight line with one spinning in the middle with θ=ωt.
    Find the intensity of light coming out the other side as a function of time.
    The attachment is the diagram of the system.

    2. Relevant equations
    Manus's Law: I = Imax cos2 θ. Where θ is the angle between the transmission axis for the two polarizers.

    3. The attempt at a solution
    Through the first two polarizers we have:
    I= Imax cos2 θ = Imax cos2 ωt
    which becomes
    I= Imax/2 (1+ cos(2ωt))

    Then the light from the second polarizer is:
    I= Imax/2 (1+ cos(2ωt)) cos2 (90-ωt)= Imax/2 (1+ cos(2ωt)) sin2 (ωt)

    and this turns into:
    Imax/4 (1+ cos(2ωt))(1- cos(2ωt))
    Imax/4 (1- cos2 (2ωt))
    Imax/4 (1-(1+cos(4ωt)/2))
    And for the answer we have:
    Imax/8 (1- cos(4ωt))

    The problem is the book expects the solution to be:
    Imax/16 (1- cos(4ωt))

    So I am off by a factor of 2. Can anyone see my problem or could it be a typo?
     

    Attached Files:

    Last edited: Sep 25, 2013
  2. jcsd
  3. Sep 25, 2013 #2

    rude man

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    Please provide the attachment.
     
  4. Sep 25, 2013 #3
    Must not have clicked upload the first time.
     
  5. Sep 25, 2013 #4

    haruspex

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    What would the intensity be with only one polariser?
     
  6. Sep 25, 2013 #5
    *face to palm* Thanks Haruspex
     
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