Electromagnetic field in a medium

1. Sep 25, 2009

Bob_for_short

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. Sep 25, 2009

Bob_for_short

Isn't it a challenging exercise?

3. Sep 26, 2009

Meir Achuz

The combination (ωt-kx) is a Lorentz invariant and so will transform to (ω't'-k'x').

4. Sep 27, 2009

Bob_for_short

Sorry, I meant cos(k'x'). In this moving reference frame the new frequency ω'=0, isn't it?

Last edited: Sep 27, 2009
5. Sep 27, 2009

Meir Achuz

No. Omega' is given by the usual relativistic Doppler in terms of v/c, which in your case would be 1/n.

6. Sep 27, 2009

Bob_for_short

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'.