Lorentz transformation of frequency

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SUMMARY

The discussion centers on the application of Lorentz transformation to the frequency of light waves reflecting off a moving mirror along the X-axis. The participants confirm that the frequency of the incoming wave (ω'1) in the mirror's frame is equal to the frequency of the reflected wave (ω'2). The key takeaway is that the frequency transformation involves converting the lab frame frequency (ω1) to the mirror frame frequency (ω1') and then back to the lab frame (ω2'), while maintaining the invariance of wave phase across different frames of reference.

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  • Understanding of Lorentz transformation equations
  • Familiarity with wave frequency and phase concepts
  • Knowledge of special relativity principles
  • Basic understanding of light wave behavior upon reflection
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Maximtopsecret
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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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