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Optics of Moving Sources

Problem 5.229

A plane electromagnetic wave of frequency ω0\omega_{0} falls normàlly on the surface of a mirror approaching with a relativistic velocity VV. Making use of the Doppler formula, find the frequency of the reflected wave. Simplify the obtained expression for the case V≪cV \ll c.

Reveal Answer
5.229.ω=ω0(1+β)/(1−β), where β=V/c;ω≈≈ω0(1+2V/c)\begin{array}{l} 5.229 . \omega=\omega_{0}(1+\beta) /(1-\beta), \quad \text { where } \quad \beta=V / c ; \quad \omega \approx \\ \approx \omega_{0}(1+2 V / c) \end{array}
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