OK I'm trying to analyse a situation in two different ways which should give the same answers but arent!
I have a rocket moving at speed 2c/3 and it emits a photon from x' which travels to the origin and then back to x' again. This obviously means t' = 2x'/c
So I want to see what time the stationary observer records, and using the standrd equation: t = gamma(t' + vx'/c^2) I obtain 4t'/root(5)
Now I wanted to check that this corresponded to length contraction, so I imagined the stationary observer seeing the rocket to be length x. That means that the first leg of the photon journey is t=x/(c+v) because it the photons relative speed to the rocket is c+v. And then adding on the return journey, t=x/(c+v) + x/(c-v)
substitute in the value for v above, to get: t=3x/5c + 3x/c = 18x/5c
But that should equal the previous calculated t, so 18x/5c = 4t'/root(5) = 8x'/croot(5)
so x = x' * (40/18root(5))
but using the standard transformation, that factor should be gamma = 3/root(5)
so where's my mistake!?