 Solution

Treat the given orbital separation as the projected separation on the sky. The small angular separation isFor an ideal circular telescope aperture of diameter $D$, the Rayleigh criterion requires $1.22\lambda /D\le \theta$. ThereforeThis is the diffraction limit, assuming comparable image brightness and adequate sampling. Atmospheric image blurring can require correction or space-based observing. A smaller actual projected separation of the binary star would require a larger aperture.