= Solution
Moving one Michelson mirror changes <optical path difference> by twice its displacement. Therefore
$$
\boxed{2d=10\lambda,\qquad d=2.50\,\mathrm{\mu m}.}
$$
For <two-wavelength Michelson rephasing>, start from a position where both colours are bright: the next simultaneous bright centre requires $2\Delta d$ to be a common integer multiple of both <wavelengths>. The smallest is $6(500\,\mathrm{nm})=5(600\,\mathrm{nm})=3.00\,\mathrm{\mu m}$, giving \b[an additional mirror movement of $1.50\,\mathrm{\mu m}$].
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