 Solution

Both the incoming and outgoing spherical wavefronts contribute to the path excess. At aperture radius $u$, with axial distances $s$ before and $r$ after the aperture,The outer edge of the $n$th Fresnel half-period zone has $\Delta \ell =n\lambda /2$. HenceTherefore the outer radius is $\boxed{u_2=4.47\times 10^{-4}\mathrm{m}=0.447\mathrm{mm}}$. The paraxial approximation is excellent because $u_2\ll s,r$. Treating the illumination as a plane wave would incorrectly omit the source-side path curvature.