A Michelson interferometer is set up in air, and light from two sources is passed through it, perpendicular to the mirrors and onto a screen. One source is an argon-ion laser with a known wavelength of 514.5 nm, and the other a monochromatic source with an unknown wavelength. It is found that at a particular mirror setting, bright fringes from the two sources overlap precisely, i.e., constructive interference occurs for both wavelengths simultaneously. One of the mirrors is then slowly moved away from the beamsplitter, and the number of bright fringes that go past on the screen are counted. It is found that 83 fringes of the argon-ion wavelength occur while 85.5 fringes of the unknown wavelength go past (i.e., the unknown wavelength ends up on a dark fringe).

(a) What was the minimum possible difference in distances of the two mirrors from the beamsplitter in the original setup, assuming that the path difference was not actually zero?