As a result of studying the regularities of interaction between polishing powder wear and sludge nanoparticles during the polishing of polymer optical materials by disperse systems of micro- and nanopowders on the basis of ab initio calculations according to the quantum scattering theory, it has been established that polishing powder wear nanoparticles are elastically scattered on sludge nanoparticles exclusively at angles of 0° and 180° over the differential scattering cross section 104–105 times larger than for other angles. It has been shown that the total cross section for the scattering of wear nanoparticles on sludge nanoparticles exponentially decreases with an increase in their average size and grows with increasing concentration. When the polymer materials are polished with disperse system DS1, the total cross section for the scattering of wear nanoparticles on sludge nanoparticles exponentially decreases with an increase in the quality factor of a resonator. When disperse system DS2 is used, the total cross section for the scattering of wear nanoparticles of sludge nanoparticles is independent of the quality factor of a resonator. It has been shown that the formation of a deposit from polishing powder wear particles on the surface of a part is most probable at maximum total scattering cross sections. It has been experimentally established that a deposit in the form of a film with a thickness of 1.5 and 0.3 µm completely or partially coats the surface of a part when polystyrene or polyallyl diglycol carbonate is polished with disperse system DS2.