Kitchen soap and a clean cotton cloth are often enough to clean and remove smudges and light scratches from plastic lenses. Deeper scratches can be remedied by using simple household products, such as baking soda or toothpaste. Just make a thick paste by combining baking soda and water. Dab a cotton cloth on the mixture, and rub it on the surface of the plastic lens until the scratch is removed.
If using toothpaste, stick to a non-whitening, non-gel toothpaste that is non-minty and non-abrasive to prevent further scratches on the lenses. Massage the surface of the lens using a cotton ball or fabric with a dab of toothpaste. Rinse with cool water, and wipe with a clean, lint-free cloth.
Other household items that can be used to remove scratches from either glass or plastic lenses are vehicle wax, silver or brass polish and furniture polish. These items help eliminate scratches by filling in the gaps created by the scratches and also giving the lenses a clear, neat polish. If using vehicle wax or silver polish, use several small pieces of square cloth, as wax sticks on fabric easily. Commercial furniture polish, such as Pledge, may only deliver a fix that lasts for a few days.