In reply to JJL:
It's easy to polish scratches out of plastic but that will cause a small optical aberration. If the scratch is deep you'll need to start with wet and dry paper, used wet, in increasingly fine grades then polish in increasingly fine grades. Something like Solvol Autosol is quite coarse and aggressive, then Brasso then car polish, which has quite a fine grain. I've had a lot of success in reviving scratched plastic watch glasses and safety specs in this way. With the finest wet and dry you'll achieve a milky finish and you can then bring that to clear with car polish.
Post edited at 08:52