I have a pair of "glasses" - the lenses are plastic and coated with a
non-glare finish. One of the lenses has become covered with many fine
scratches. (I've never polished them with anything other than cotton, and
I've no idea why one lens is so bad).

Can I polish the lens myself? I have a rock-tumbling kit with all the
powders. I thought of replacing the lens , but the price was a staggering
$199.

My health plan kicks in six weeks - so I'm loathe to buy new specs now.

Killinchy wrote:

I have a pair of "glasses" - the lenses are plastic and coated with a
non-glare finish. One of the lenses has become covered with many fine
scratches. (I've never polished them with anything other than cotton,
and
I've no idea why one lens is so bad).

It could be a failed coating. These sometimes fail in a way that looks
kind of like failed varnish. If the lenses are less than a year old,
return to your optician and see if the coating failed, and if so, will
the shop replace them for free. Anti-reflective (AR) coatings often
have a 1 or 2 year warranty, at least in the US.

On the other hand, if you polish the lenses dry, it could be just that
you've scratched the lenses. AR coated lenses should be cleaned in
running water before touching them with a drying cloth. The
micro-fibre cloths are good for drying.

Can I polish the lens myself? I have a rock-tumbling kit with all the
powders. I thought of replacing the lens , but the price was a
staggering
$199.

I've heard of people trying to do this, but I doubt it succeeds.
Especially with an AR coating.

Your optician might be able to remove the coating on the lenses; if
the scratches are just in the coating, that might improve things.
Whether the coating can be removed or not depends on the type of lens
material and the coating, consult your optician.

My health plan kicks in six weeks - so I'm loathe to buy new specs now.

Personally, I would wait out the 6 weeks. :)

Repost this question in sci.med.vision, and you'll get more expert
replies. That's where the optician type folks hang out. If you know
what material the lenses are, and what kind (brand) coating you have,
that will help.

Terry