if you rub two things together, there are only two shapes which could possibly remain in constant contact. the first is perfectly flat which is very hard with o

if you rub two things together, there are only two shapes which could possibly remain in constant contact. the first is perfectly flat which is very hard with only two surfaces (easier with three) the second is hemispheres and if you do the easiest thing possible rubbing two things together they will wear one another into matching convex and concave hemispheres. for some optics that is close enough (small diameter long focal length e.g. a 6" F8) otherwise instead of a spherical surface you may need a paraboloid (or other aspheric)in which case you need to preferentially deepen some part of the curve (~70% of the radius) a few millionths of an inch. but when you do it wrong you go back to doing the easy thing and make it spherical then try again... and again ... and again ... (but I'm not bitter). Till you decide it is good enough! The minimum standard for good enough is a under a quarter wavelength in the short end of the spectrum of interest . this is because an extra quarter down plus the same quarter back up and you are a half wave out with another part of the mirror which when combined by your eye results in destructive interference of both parts of the mirror. one last point on the final smoothness, the interplay of glass, water, pitch, metal oxide and mechanical force is imperfectly understood. crudely it may be closer to planing than grinding but that does not explain the oxide particles which are found beneath the surface of a figured mirror. another thought is the an atom in the glass is "stretched" up and snaps back into a lower energy configuration which is more atomically flat