to remove scratches, from say, a Scotchbrite pad? (Don't ask...)
If you can feel the scratches with your fingernail, probably not. If they're smaller than that you may be able to polish them out, but it's time consuming and the results may not be very satisfactory. Places like The Eastwood Company sell glass polishing kits that use cerium oxide as the polishing media.
I've seen it done using cerium oxide on one of those Velocity concourse preparation type shows. Supposedly it works pretty well if you're just talking small and medium scratches. I suspect it'll do the job on Scotchbrite level scratches.
There's supposed to be something more aggressive but I'm coming up a bit short on the source at the moment.
If you have a "fuzzy" windshield, yes. The little scratches that get in it over time from things like dirt on the wipers or dust hitting the glass on the road, yes.
Basically, if you can only see the scratches with oncoming headlights or sun glare, they can be polished.
A real scratch can't be. You would need to sand/grind with a diamond wheel and go through a rigorous, labor-intensive process and you would be left with a lens. That section will be distorted like looking through someone else's glasses.
Eastwood sells an oxide glass polishing kit. It comes with an orange powder that you mix with water to make a paste and a polishing pad. Works well on the light hairlines and mineral spots, but it won't take out a scratch that you can feel with your fingernail.
I see Eastwood now has a heavy duty kit for deeper scratches, but I would be skeptical about how well it works. https://www.eastwood.com/glass-polishing-kit-for-deep-scratches-5658.html
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