•Arrival time for first
photon: t1 = d/c
•2nd photon: t2 = te + (d-vte cosφ)/c
•Δt = t2- t1 = te (1 – (v/c)cos φ)
•Note that this time is shorter than te.
•Apparent transverse
velocity is then:
–vapparent =vtesinφ/ Δt = vsin φ/(1-(v/c)cos φ)
•Solve for v/c = (vapp/c)/(sin
φ+(vapp/c)cos φ)
•You can go on from here to determine things about the angle, minimum velocities,
Lorentz factors, etc. (Hint
good to look at for exam/qualifier questions).