 Solution

ID: past-exam-of-the-physics-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/b4/a/solution

In the instantaneous mirror frame the incident frequency is

f_{m} = γ (1 - β) f

. Ideal reflection reverses propagation without changing that frame's frequency. Transforming the backward photon to Earth gives another factor

γ (1 - β)

f_{r} = γ^{2} (1 - β)^{2} f = \frac{1 - β}{1 + β} f .

This uses a classical mirror with negligible recoil per individual photon.

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