= Solution
For an object near the front focal plane, the objective's <numerical aperture> in air is
$$
\mathrm{NA}=\sin\theta\simeq\frac{D}{2f}=\frac{0.005}{2(0.020)}=0.125.
$$
The <Rayleigh criterion> for a circular objective gives object-space <diffraction-limited resolution>
$$
\boxed{\Delta x\simeq\frac{0.61\lambda}{\mathrm{NA}}=\frac{1.22\lambda f}{D}=2.93\times10^{-6}\,\mathrm m\simeq2.9\,\mathrm{\mu m}}.
$$
The factor $1.22$ comes from the first zero of the <Airy disk>. Using the exact $\sin(\arctan(D/(2f)))$ changes the result by less than $1\%$. A coarser $\lambda f/D$ estimate gives $2.4\,\mathrm{\mu m}$; the chosen criterion must be stated. This estimates the <aperture> limit, before aberrations and detector sampling.
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