Ranjit belongs to an astronomy club, and the club owns a telescope with an objective of diameter…

Ranjit belongs to an astronomy club, and the club owns a telescope with an objective of diameter $0.30\ \text{m}$. On a clear night he looks at the Moon in green light of wavelength $550\ \text{nm}$, and he wants to know how small a feature he could ever hope to see there. The Moon is $3.84 \times 10^{8}\ \text{m}$ away. The pupil of the unaided eye is $3.0\ \text{mm}$ across, in the same light. His friend would like to compare the answer with the size of a town, so the sizes must be in metre. Find the smallest angle that the telescope can separate, in arcsecond. Find the smallest feature on the Moon that it can separate. Find how many times larger the smallest feature is for the unaided eye. Then explain why Ranjit cannot see a smaller feature by fitting an eyepiece of a shorter focal length, which would only make every image larger, and say what would help instead. Use $\theta = \dfrac{1.22\,\lambda}{D}$ and one arcsecond $= 4.85 \times 10^{-6}\ \text{rad}$.