The prescription specs which I use for computer-based activities have a scuff mark about the size a finger-print from a little finger on one of the (plastic) lenses.
Whilst I could buy a new lens for £30 or so, I've been trying to polish it out on a DIY basis.
I tried Brasso but didn't do a lot because the blemish was a bit too deep. I then rubbed the area very gently with very fine wet & dry, used wet. This got rid of the scratches, but left the area looking like frosted glass. I've improved it quite a lot by buffing it with a dremel-like tool, using a buffing paste made from olive oil and talcum powder (how DIY can you get!) followed by a further application of Brasso. The affected area is still a bit blurry.
Any ideas of what else to try?