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Fresnel Equations

  1. Mar 14, 2012 #1
    Hi guys!

    Was wondering if anyone was confident with Fresnel equations for a refractive index interface. From what I understand:

    Assume incoming normal plane wave travelling in z-direction and polarised in x plane.

    Assume z=0 is the plane that separates two materials: n_1 and n_2 (refractive index)

    I think the Fresnel solution for the wave should go:

    Ex = (for z>0) exp(-i*k0*n_1*z)+r*exp(i*k0*n_1*z)

    (for z<0) t*exp(-i*k0*n_2*z)

    the RED term representing the normal incident component and the GREEN term represents the reflected component which only exist in the n_1 half

    and the BLUE term representing the transmitted component which only exists in the n_2 half.

    I am uncertain about if I should be adding both the incident and reflected term (for z>0) as long as they are travelling in different directions or if I need to subtract them. i.e. should it be RED+GREEN or RED-GREEN? As I already have defined them to travel in opposite directions.

    Any thoughts?

    Many thanks!
  2. jcsd
  3. Mar 14, 2012 #2


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    You find the coefficients by solving for the boundary conditions at the surface between the two media. This can be found in any textbook on electrodynamics or optics.
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