By Fraunhofer diffraction through a circular aperture, $\mathrm{\theta }=\frac{1.22\mathrm{\lambda }}{d}$

$d=$ diameter of pupil $=2\times \text{0.25}=\text{0.5}\mathrm{ }\mathrm{cm}$
$\mathrm{\lambda }=500\mathrm{ }\mathrm{nm}$. The first dark ring is formed by the light diffracted from the hole at an angle $\mathrm{\theta }$ with the axis. Viewing distance, $D=25 \mathrm{cm}$$\therefore$ The minimum separation between $2$ objects $=D\theta$$=\frac{25\times {10}^{-2}\times 1.22\times 500\times {10}^{-9}}{5\times {10}^{-3}} \mathrm{m}$
$D\theta =30\times {10}^{-6} \mathrm{m}$$\Rightarrow D\theta =30\mathrm{ }\mathrm{\mu m}$.