Past exam of the short options course of the University of Oxford / 2021 / 8 / c / ii

For a photon, $m=0$ and $u=c$, so the result from (i) reduces toThis is relativistic aberration for a photon initially transverse to the boost. It also follows directly from $p_x^{\prime }=\gamma VE/c^2$ and $E^{\prime }=\gamma E$: the observed direction cosine is $c{p}_x^{\prime }/E^{\prime }=V/c$. The transverse observed speed is $c/\gamma =c\sin \varphi$, and the total photon speed is still $c$. If desired the observed photon energy is $E^{\prime }=E/\sin \varphi$ for $0<\varphi \le \pi /2$.