= Solution
The <Rayleigh criterion> gives a separation in the sensor plane $\delta=f\Delta\theta=2.44\,\mu\mathrm m$, using the $5\,\mathrm{mm}$ image distance. Counting one square <pixel> per such <spatial resolution element> gives
$$
\boxed{N_{\rm Rayleigh}\simeq\frac{(4\,\mathrm{mm})(3\,\mathrm{mm})}{(2.44\,\mu\mathrm m)^2}=2.02\times10^6.}
$$
This is an estimate of the number of optically distinguishable elements. To sample all the spatial information, specify a <signal sampling> criterion as well. For <incoherent imaging> through an ideal circular <aperture>, the <optical transfer function> has cutoff spatial frequency $\nu_c=D/(\lambda f)$. The <Nyquist–Shannon sampling theorem> requires a <pixel> pitch
$$
p\leq\frac1{2\nu_c}=\frac{\lambda f}{2D}=1.00\,\mu\mathrm m,
\qquad \boxed{N_{\rm Nyquist}\geq4000\times3000=1.20\times10^7.}
$$
A common intermediate rule, two <pixels> per Rayleigh separation, gives about $8.1$ million <pixels>; it is a heuristic and does not quite sample the full ideal <optical transfer function> bandwidth. Thus about $2$ million is the elementary <spatial resolution element> count, while $12$ million is the ideal monochrome <Nyquist–Shannon sampling theorem> answer to “full use.” Color-filter layout and finite <pixel> area would impose further practical conditions.
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