I think that would mean only a dyson hemisphere, since Earth is illumnated by the entire hemisphere of the sun that faces us, due to the sun's sheer size.

To see the kinds of effects this would have on the gas giants would be fascinating. It would probably drastically alter the coriolis banding and spots on Jupiter and Saturn.

Venus would probably be the only other planet affected, and perhaps comet behavior might change. In fact, I wonder if planets would become so cold, that they might produce visible comas as they warm up, when they enter the sun's (now hemispherical) light cone. That's probably the most prominent effect I can see happening.