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Clean the surface of your lenses in order to determine where the scratches actually are. Apply scratch remover to your lenses. Wipe off any excess scratch remover. Try another cleaner if toothpaste or baking soda did not work. Apply a scratch filling product if scratches remain. Put your glasses back on!
Make sure to use a cleaner made specifically for glasses and a clean micro-fiber cloth. You can get this at any eye glass store or optometrist's office. In fact, they will probably give it to you for free if you have bought glasses there. There are a wide variety of products that can be used to remove scratches to your lenses. Begin by dabbing a non-abrasive toothpaste on the lens. Rub it on the scratch in a circular motion with a cotton ball and rinse it with cool water. If the scratch is deep, you may need to repeat the process a few times. If you don't have non-abrasive toothpaste you can make a paste from baking soda and water. Put baking soda in a bowl and mix in small amounts of water until you have a thick paste. Rub the paste on the same way you did the toothpaste, and rinse it off when you think the scratch is gone. If you cannot remove it all with a rag or a cotton ball, rinse the lenses with cool water and wipe dry with a non-abrasive rag. Try buffing the scratched plastic glasses with brass or silver polish and a soft rag. Rub the polish around on the glasses and wipe any excess off with a clean, soft rag. Repeat until the scratch is gone. Be careful of your glasses frames when using a cleaner that is not made for glasses. Try not to get any on your frames because it is unknown what the cleaner will do to the frames. If you still have visible scratches on the surface of your plastic lenses you can apply a product that will fill the scratches temporarily with wax.  Simply rub on the product onto the lenses using a clean micro-fiber cloth, rub it around in a circular motion, and then wipe it off with a clean area of the cloth. This will allow you to see clearly through your glasses but will need to be reapplied weekly. The two types of products that work best for this are products made to wax your car, such as Turtle Wax, and furniture polishes that contains wax, such as Lemon Pledge. You should be able to see much better through your newly repaired lenses.