Past exam of the physics 1 paper of the University of Oxford / 2015 / 11 / a / Solution

Use the tunnel frame $S$, with the entrance at $x=0$, the far end at $x=L$, and $t=0$ at both runner entry and photon emission. The runner has $x_R=vt$, while the approaching photon has $x_{\gamma }=L-ct$. At detection,For $0<v<c$, $0<f<1/2$: the photon meets the runner before the runner reaches the tunnel midpoint.