 Solution

For viewing near the nadir, the required angular resolution isUsing 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 isThe 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 $D_{\min }=0.12298\mathrm{m}\simeq 12.3\mathrm{cm}$. The question does not specify mirror shape; $10.1\mathrm{cm}$ follows the slit-width model of part (i).