I bought a kit to resurface my acrylic headlight covers. The alternative was spending $225 for each light, or to continue to drive around with this cataract-like cloud over the eyes of my van. The bottom picture was before the treatment, the top picture was after.
The treatment consisted of sanding with 500 grit sandpaper on the end of a drill, then switching to 800 grit, then a wet sand, and finally a polish. It was four steps of successively fine grinding, and it worked pretty well, as you can see.
I was so full of success I tried it on David's contacts while they were still in his eyes. OK, not really. But I am thinking about trying it on some scratched up CDs. I'll let you know if it works.