Lorentz transformation of frequency

AI Thread Summary
The discussion focuses on applying the Lorentz transformation to determine the frequency change of a light wave reflecting off a moving mirror. It establishes that the frequency of the incoming wave in the mirror's frame (ω'1) is equal to the frequency of the reflected wave (ω'2) in that same frame. The participants agree on the need to convert the frequency from the lab frame to the mirror frame and back, emphasizing that the wave phase remains invariant across different observers. The key takeaway is that the transformation correctly accounts for the frequency change due to the mirror's motion. Overall, the application of the Lorentz transformation in this context appears to be validated.
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Homework Statement


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.

Homework Equations


I know Lorenz transformation for frequency.

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?
 
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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.
 
MarcusAgrippa said:
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.
IMG_20150602_184117.JPG


Should it be like that?
 
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