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

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- Solution 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} = v t

, while the approaching photon has

x_{γ} = L - c t

. At detection,

t_{D} = \frac{L}{c + v}, x_{D} = \frac{vL}{c + v}, f = \frac{x _{D}}{L} = \frac{v}{c + v} = \frac{β}{1 + β}, β = \frac{v}{c} .

For

0 < v < c

,

0 < f < 1/2

: the photon meets the runner before the runner reaches the tunnel midpoint.

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