All Problems Thermal Radiation. Quantum Nature of Light.
Problem 5.267
In a reference frame \(K\) a photon of frequency \(\omega\) 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 \(K\).
5.267. (a) \(\Delta p=\frac{2 \hbar \omega}{c} \frac{\sqrt{1-\beta^{2}}}{1-\beta}\) (b) \(\Delta p=\frac{2 \hbar \omega}{c} \frac{1}{1-\beta} . \quad\) Here \(\quad \beta=\) \(=V / c .\) It is evident that in the reference frame fixed to the mirror the latter obtains the smaller momentum.