All Problems

Thermal Radiation. Quantum Nature of Light.

Problem 5.267

In a reference frame KK a photon of frequency ω\omega falls normally on a mirror approaching it with relativistic velocity VV. 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 KK.

Reveal Answer
5.267. (a) Δp=2ωc1β21β\Delta p=\frac{2 \hbar \omega}{c} \frac{\sqrt{1-\beta^{2}}}{1-\beta} (b) Δp=2ωc11β.\Delta p=\frac{2 \hbar \omega}{c} \frac{1}{1-\beta} . \quad Here β=\quad \beta= =V/c.=V / c . It is evident that in the reference frame fixed to the mirror the latter obtains the smaller momentum.