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Homework Help: Show that the real and imaginary parts of the wavenumber, k, are given by

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that the real and imaginary parts of the wavenumber, k, are given by
    k(real)=[sqrt(epsilon(real))]omega/c

    and k(imaginary)=[epsilon(imaginary) *omega/(2c sqrt(espilon(real)))

    3. The attempt at a solution

    k^2= mu epsilon omega^2 (1+(i g/epsilon*omega))
    k^2 (real)=sqrt (mu epsilon omega^2)
    =sqrt(mu epsilon)*omega
    =sqrt(mu epsilon(real) epsilon0) omega
    =(1/c)sqrt(epsilon(real)) omega

    k^imaginary =(mu epsilon omega^2 i g)/(epsilon omega)
    =mu omega i g
    g is approximately epsilon omega
    k^2(imaginary)=mu omega i epsilon omega
    k=sqrt(mu epsilon) omega sqrt(i)
    =(1/c) omega sqrt(i)
    =(1/c) omega (1/(sqrt(2)))(1+i)
     
  2. jcsd
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