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Cross Polarizers with a wave plate retardation

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data
    "Consider a wave plate with a retardation τ=(η_0-n_e)*w*L/c. Show that when it is placed between crossed polarizers with its optical axis at an angle of θ with respect to the polarizer axis, the transmitted intensity is given by:

    I_out/I_in= (sin^2(2θ)(sin^2(τ/2))

    In practice, one often sets the optical axis at θ=45° to obtain maximum contrast.


    2. Relevant equations


    E=P_θ*P_0*E_0


    I=E times E*


    3. The attempt at a solution

    I know that without any retardation I/I_0=cos^2(θ). I'm really not sure how to approach this problem
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 15, 2012 #2

    rude man

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    Homework Helper
    Gold Member

    Let's start by rewriting your given equations:

    ψ = (n_o - n_e)Lω/c

    since ψ is a radian angle so τ is not a good symbol since it usually has dimensions of time.

    Then Io/Ii = sin2(2θ)sin2(ψ/2)

    So you have one sinusoidally time-varying electric vector field Eo that passes thru the plate and then thru the polarizer and analyzer, and a second field Ee that does the same but is phase-shifted by ψ radians w/r/t Eo and is perpendicular to it.

    Then at the output of the analyzer, add the two fields vectorially, then square and time-average to get the intensity, & off you go.
     
  4. Oct 30, 2012 #3
    Thank you very much, that helps a lot!
     
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