 Two-wavelength Michelson rephasing

Moving one mirror by $d$ changes the round-trip optical path by $2d$. Starting at a common bright centre for two commensurate wavelengths, the next common bright centre occurs when $2d=m{\lambda }_1=n{\lambda }_2$ for the smallest positive integers. This is a common-multiple condition on optical path, not on the mirror displacement itself. Incommensurate exact wavelengths have no finite exact recurrence in the ideal model.