Recently I stripped some old sextant mirrors prior to re-silvering them. Since they were all from sextants of well-known makes and presumably satisfied their users, I thought to see just how flat the silvered surfaces were.
I placed them on an optical flat that had been made by the same person who ground the 1 metre telescope mirror of the Mount St John Observatory in New Zealand and illuminated them with an extended source of green light light from mercury lamps. The flat is known to be flat to within one tenth of a wavelength.
Without going into why we see interference bands, we can say that the dark lines you see represent contour lines on the mirrors, at intervals of half a wavelength. Perfectly straight, evenly spaced lines represent a flat surface. I have added a white line to help in seeing by how much some of the lines deviate from straightness (the coarser bands in the background are outlines of the battery of lamps). None deviated by more than half a wavelength.
I have in the recent past replaced old mirrors with new ones cut for a few dollars from pieces 4 mm-thick modern float mirror glass, without being able to detect any loss of performance. I wondered how it would compare with the optically worked examples from the past, so I stripped a piece to try it. The following image shows that it compares very well and offers a much cheaper solution than buying a new one, often for several tens of dollars. So how flat do sextant mirrors need to be?
P.S. Visit NavList for February 09 to see some responses to this question.