 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2021/8/c/ii/solution

m = 0

and

u = c

, so the result from (i) reduces to

V = c cos ϕ, v_{O} = - c cos ϕ e_{x} .

This is relativistic aberration for a photon initially transverse to the boost. It also follows directly from

p_{x}^{'} = γV E / c^{2}

and

E^{'} = γ E

: the observed direction cosine is

c p_{x}^{'} / E^{'} = V / c

. The transverse observed speed is

c / γ = c sin ϕ

, and the total photon speed is still

c

. If desired the observed photon energy is

E^{'} = E / sin ϕ

for

0 < ϕ \leq π /2

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