# Lorentz transformation of frequency

1. Jun 1, 2015

### Maximtopsecret

1. The problem statement, all variables and given/known data
Light (plane wave) reflects from the mirror moving along X-axis with speed V. The wave is orthogonal to the mirror (φ=0°).
Write the law for frequency change.
2. Relevant equations
I know Lorenz transformation for frequency.
3. The attempt at a solution
All I do not know is how to apply the mentioned equation. I suppose if we denote ω'1 is the frequency of a falling wave in the mirror's system, ω'2 is the frequency of a reflected wave in that system, ω'1 = ω'2. Also I suppose ω'2 will be equal to the frequency of reflected wave in the stationary system. Am I wrong?

2. Jun 2, 2015

### MarcusAgrippa

Convert the frequency $\omega_1$ of the wave in the lab frame to $\omega_1'$ in the frame of the mirror. The, as you correctly state, the reflected wave has $\omega_2' = \omega_1'$. Convert the frequency $\omega_2'$ of the wave in the mirror frame back to the lab frame. The conversion is done by noting that the wave phase is an absolute invariant - all observers agree on what is a crest and a trough.

3. Jun 2, 2015

### Maximtopsecret

Should it be like that?

4. Jun 2, 2015