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Using Fresnel Formulae and Poynting vector problem

  1. Feb 23, 2016 #1
    1. The problem statement, all variables and given/known data
    I'm having a problem using the fresnel formulae for these two problems below:

    1. Using Fresnel formulae and expression for the Poynting vector show that at the interface between two dielectrics in the absence of absorption R+T=1, where R – is reflectivity and T – transmissivity

    2. Using Fresnel formulae, find expressions for the amplitudes and intensities of the reflected and transmitted plane electromagnetic waves incident normally at an interface between two materials with refractive indices n1 and n2

    2. Relevant equations

    I know reflectivity is given by R = j(r)/j(i) = ∣R^2∣/∣A^2∣
    and transmissivity is given by T = j(t)/j(i) = (n2/n1)*(cosθt/cosθi)* ∣T^2∣/∣A^2∣

    and the Poynting vector is: S = EH = 1/(v*μ0*E^2) = n*c*ϵ0*E^2

    given that:

    J(i) = S(i)cosθi = n1*c*ϵ0*∣A^2∣*cosθi

    J(r) = S(r)cosθi = n1*c*ϵ0*∣R^2∣*cosθi

    and J(t) = S(t)cosθi = n2*c*ϵ0*∣T^2∣*cosθi


    3. The attempt at a solution

    In theory, I can prove that R+T=1 but I am struggling with the fractions as they have always been my worst enemy throughout university. If someone can help me out with this please I would appreciate it. My main problem is working this using the 'conservation of energy', which I don't understand where the conservation of energy comes into place for this question, and why we need it to prove R+T=1.

    For the second question I am struggling to understand it at all, when it talks about incident normally to the plane. We haven't covered waves being incident parallel or perpendicular between two materials at all.



    Any help and insight will be greatly appreciated!

    Thanks,

    Tom
     
  2. jcsd
  3. Feb 28, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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