 Solution

The first single-slit minimum is at $\sin \theta =\lambda /w$, so the characteristic angular resolution of an aperture of width $D$ is of order $\lambda /D$. With $D=1$ m, $\lambda =550$ nm, and distance $\mathcal{D}=10^8$ m, this slit-based estimate isFor the actual circular lens, the Rayleigh criterion uses the first zero of the Airy disk, $\Delta \theta \simeq 1.22\lambda /D$. It gives $6.71\times 10^{-7}$ rad and a resolved separation of about $67$ m. The factor $1.22$ belongs to the circular aperture, not to the one-dimensional slit derivation.