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



d = diameter of pupil $=2\times \text{0.25}=\text{0.5}\mathrm{ }\mathrm{cm}$

$\mathrm{\lambda }=500\mathrm{ }\mathrm{nm}$

First dark ring is formed by the light diffracted from the hole at an angle $\mathrm{\theta }$ with the axis.

Viewing distance, $\mathrm{D}=25 \mathrm{cm}$

$\therefore$ Minimum separation between $2$ objects $=\mathrm{D\theta }$

$=\frac{25\times {10}^{-2}\times 1.22\times 500\times {10}^{-9}}{5\times {10}^{-1}}$

$=30\times {10}^{-6} \mathrm{m}$

$=30\mathrm{ }\mathrm{\mu m}$