A Question for the Chemistry Geeks and Auto Buffs Out There

The plastic covers over my headlights are becoming opaque. Not the best situation. There are products out there that promise to restore that plastic to its virtually-invisible former self, but as far as I can tell all those products simply polish the surface of the plastic. It seems to me the damage is cause by ultraviolet radiation and likely goes more than skin deep.

Still, I’d like to believe the commercials that say they can restore my headlight covers to their former optic glory. I just don’t want to spend the precious cash dollars to find the claims to be bogus. Is there anyone out there who can either a) explain or b) attest to the worthiness of these products?