= 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 is
$$
\boxed{\Delta\theta\sim5.5\times10^{-7}\,\mathrm{rad},\qquad \Delta x\sim55\,\mathrm m.}
$$
For the actual circular lens, the <Rayleigh criterion> uses the first zero of the <Airy disk>, $\Delta\theta\simeq1.22\lambda/D$. It gives $6.71\times10^{-7}$ 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.
\Image[/past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2013-resit-single-slit.png]
{title=Far-field single-slit intensity and the first diffraction minima}
{description=The horizontal coordinate is w sin(theta)/lambda, so the first zeros are at plus and minus one. The lens-resolution estimate uses the central-maximum width.}
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