Two flashes of light strike at the same time, at the two orange circles on the diagram. The green train is traveling at a constant 150 kmh relative to the grey platform. The train is 1 km long.
As measured by someone at point F on the grey platform, how much time passes between the arrival of the waves at F’ on the train? (basically, the 2nd and 4th picture):
x = γ(x’ + vt’)
t’ = γ(t – vx/c2)
γ = (1 – v2/c2)-1/2
The Attempt at a Solution
Since they will arrive at exactly the same time for an observer on the train at F’, t = 0. t' will be the difference.
t’ = γ [0 – vγ(vt’)/c^2]
where v = 41.66666, and γ = 1.00000000000001
I’d like to hear any feedback on if I’m on the right track before trying to solve for t’.