Lord J. W. S. Rayleigh (1842-1919), the Nobel Prize-winning English
physicist, empirically determined that telescope optics that yield 1/4th
wave accuracy at the final focus (so that all light gathered by the
system comes to a focus within 1/4th of a wavelength of the green light
to which the eye is most sensitive) will produce results on stars that
are visually indistinguishable from an optically perfect system. This is
known as the Rayleigh Criterion and is a handy yardstick by which
telescope quality can be measured. To achieve a 1/4th wave accuracy
overall, each mirror in a reflector must be finished to 1/8th wave
smoothness. When observing extended deep space objects (such as nebulas
and galaxies), most amateur astronomers find it difficult to see any
visible difference between optics made to 1/4th wave accuracy and those
made to 1/10th wave accuracy - although experienced observers usually
find the higher accuracy to be beneficial on planets. Large optics
polished to higher levels of accuracy than 1/10th wave usually gain the
observer little additional benefit visually, however, as the performance
of the telescope will be limited more by atmospheric conditions than it
will be by mirror accuracy. Inexpensive scopes can have mirrors
polished to 1/4th wave accuracy and still have a rough surface marred by
micro-ripple whose errors might be 1/50th wave or less. Such rough
mirrors will have visibly lower contrast and less-sharp images than a
well-finished mirror.