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When he shines it forward, I assume the outside observer sees the ship moving at .5c and the beam moving at c, which means he sees the beam move away from the ship a distance of about 150,000 km after 1 second.

The observer in the ship has a shortened ruler and a slower clock compared to the outside observer, so for him the beam has traveled more than 150,000 km away and taken less time to do it because of his slower clock. The combination of these two things assures him that the beam is traveling at speed c.

But if he shines the light out the back of the spaceship, the outside observer will see that the light has separated from the ship by 450,000 km after one second. If the observer on the ship has a shorter ruler and slower clock, it seems like he would perceive that the light has traveled further than 450,000 km in less than 1 second.

I know this is obviously the wrong way to look at it, since the guy on the ship has to see it as traveling at speed c regardless of which direction he shines it.