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_{0}
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]

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_{0}
If the particle and lightbulb are at relative rest, how can they pass each other?

[Reikoku]

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

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]

I meant to say that the particle is moving with 0.5c compared to the lightbulb.
OK.
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.
Yes.

[Reikoku]

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