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Homework Help: Polarization of Reflected Beam

  1. Apr 23, 2012 #1
    1. The problem statement, all variables and given/known data

    A beam of light travelling in air hits a glass surface with refractive index 1.5 at 45 degree angle. The light is polarised at 45 degrees with respect to the plane of incidence. Calculate the polarization of the reflected beam.


    2. Relevant equations

    Boundary Conditions: E[itex]_{1}[/itex][itex]^{||}[/itex] = E[itex]_{2}[/itex][itex]^{||}[/itex] and [itex]\mu_{2}[/itex]B[itex]_{1}[/itex][itex]^{||}[/itex] = [itex]\mu_{1}[/itex]B[itex]_{2}[/itex][itex]^{||}[/itex]

    Also, from the polarization: E[itex]_{I}[/itex][itex]^{||}[/itex] = E[itex]_{I}[/itex][itex]^{\bot}[/itex]


    3. The attempt at a solution

    I apply the first boundary condition to obtain E[itex]_{I}[/itex]cos45 + E[itex]_{R}[/itex]cos45 = E[itex]_{T}[/itex]cosθ.
    I suppose i can do the same thing using the second boundary condition. I dont really understand how to compute the polarization of the reflected beam. Am i suppose to calculate the reflection coefficient to determine the polarization. Also, how does the initial polarization of 45 degree plays a part here. Thanks.
     
  2. jcsd
  3. Apr 25, 2012 #2

    rude man

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    Homework Helper
    Gold Member

    Split the incoming electric field (forget the B field altogether) into σ ad π components. The σ component is parallel to the glass surface. The π component is orthogonal to the direction of propagation and the σ component.

    Then apply the rules for σ and π reflection percentage as a function of the angle of incidence.

    This link is a huge help:
    http://www.physics.rutgers.edu/ugrad/389/FresnelsEqns.ppt#257,1,Fresnel's Equations for Reflection and Refraction
     
    Last edited: Apr 25, 2012
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