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Electromagnetic field in a medium

  1. Sep 25, 2009 #1
    An electromagnetic field, as a plane wave, has a known space-time dependence:

    E = E0cos(ωt-kx).

    In a transparent medium it is the same except for involving the refraction indices n.

    Now, let us look at the field in a moving reference frame - that with v = c/n. What solution is for the wave in such a frame? Isn't it

    E' = E'0cos(ω't') ?
     
  2. jcsd
  3. Sep 25, 2009 #2
    Isn't it a challenging exercise?
     
  4. Sep 26, 2009 #3

    Meir Achuz

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    The combination (ωt-kx) is a Lorentz invariant and so will transform to (ω't'-k'x').
     
  5. Sep 27, 2009 #4
    Sorry, I meant cos(k'x'). In this moving reference frame the new frequency ω'=0, isn't it?
     
    Last edited: Sep 27, 2009
  6. Sep 27, 2009 #5

    Meir Achuz

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    No. Omega' is given by the usual relativistic Doppler in terms of v/c, which in your case would be 1/n.
     
  7. Sep 27, 2009 #6
    Strange. As soon as ω and k are connected via c and n>1, there should be the reference frame with the zero frequency ω'.
     
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