Abstract: A method and apparatus is provided for machine polishing plastic ophthalmic lenses to a translucent finish using a polishing wheel with 7 micron or less sized diamond particles held in a binder, such as a resin or bronze. The polishing wheels of the present invention may be in the form of a wheel for polishing edges of the lenses, or a wheel called a generator tool or bell for polishing the optical surfaces of the lenses. Either form of wheel may also be used on glass lenses. Each form may be used on a special ophthalmic machine adapted for its use, which may be capable of automatic or semi-automatic operation, to easily and quickly produce finished lenses. With the generator form polishing wheel of the present invention, a new type ophthalmic machine may be made using generator tools for both forming or cutting and finer finishing or polishing the optical surfaces of either, or both, plastic and glass lenses.