Distance light travels in a relatively moving frame?

Reikoku

I was wondering if say.. you have a particle moving at 0.5c in the +x direction and a lightbulb at relative rest to the particle.
The particle passes the lightbulb at t[itex]_{0}[/itex]
The lightbulb then flashes, the wave reaches the particle at a particular point, and the speed of light is then measured (by the particle) to be c. Does this then mean that the light wave will then travel a distance of ct from that point in the reference frame of the particle; t being any point in time that the particle wishes to measure the distance of the light wave from it.

Doc Al

If the particle and lightbulb are at relative rest, how can they pass each other?

Reikoku

Oh am I using the wrong terminology? I meant to say that the particle is moving with 0.5c compared to the lightbulb.

Doc Al

OK.
Yes.

Reikoku

Thanks Doc Al, that's helped clear up confusion.