Frequency of Reflected light in special relativity

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SUMMARY

The discussion focuses on the application of the Doppler effect in special relativity, specifically regarding the frequency of reflected light in different frames of reference. In frame K, the Doppler effect is applied twice to account for the frequency changes of light as it reflects off a mirror. The participants clarify that in the mirror frame, light pulses have a frequency denoted as ##f'##, and they seek to understand how these frequencies translate back to frame K. The confusion arises from the direction of photon movement and the corresponding signs in the frequency calculations.

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Homework Statement
In a reference frame K a photon of frequency f falls normally on a mirror approaching it with relativistic velocity v. Find the momentum imparted to the mirror during the reflection of the photon (a) in the reference frame fixed to the mirror; (b) in the frame K.
Relevant Equations
f'/f = sqrt((1+(v/c))/(1-(v/c)))
In the. solution attached I'm not too sure why in frame K, we apply the doppler effect twice. Also, since the photon is moving away from the source, shouldn't the signs be switched? Thanks
Screenshot 2024-09-24 at 10.21.05 PM.png
 
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Your image is hard to read, but you seem to have the right answer in the mirror frame. So in that frame you have left- and right-going light of frequency ##f'##. What frequency will those pulses have in ##K##?
 
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