= Solution
For viewing near the nadir, the required <angular resolution> is
$$
\delta\theta\simeq\frac{s}{H}=\frac{100}{840000}=1.19048\times10^{-4}\,\mathrm{rad}.
$$
Using the <Rayleigh criterion> with the first minimum of the <single-slit diffraction> pattern gives $\delta\theta\simeq\lambda/w$. Thus the minimum collecting width in that model is
$$
\boxed{w_{\min}=\frac{\lambda H}{s}=\frac{12\times10^{-6}\times840000}{100}\,\mathrm m=0.1008\,\mathrm m\simeq10.1\,\mathrm{cm}.}
$$
The numerical coefficient depends on the aperture shape and the chosen resolution criterion. If the mirror has an unobstructed circular aperture, the <Airy disk> version of the <Rayleigh criterion> is $\delta\theta=1.22\lambda/D$, giving $D_{\min}=0.12298\,\mathrm m\simeq12.3\,\mathrm{cm}$. The question does not specify mirror shape; $10.1\,\mathrm{cm}$ follows the slit-width model of part (i).
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