Electromagnetic field in a medium

[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') ?

 

[Bob_for_short]

Isn't it a challenging exercise?

 

[Meir Achuz]

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

 

[Bob_for_short]

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

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

 

[Meir Achuz]

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

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

 

[Bob_for_short]

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

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'.