The distance of the moon from earth is 3$.8×10^5 km$. The eye is most sensitive to light of wavelength 5500 Å. The separation of two points on the moon that can be resolved by a 500 cm telescope will be

51 m

$\text{Resolving Power } = \frac{1}{\Delta \theta} = \frac{d}{1.22\lambda}$

$ \Delta \theta = \frac{x}{r} =  \frac{d}{1.22\lambda}$

$\Rightarrow x = \frac{dr}{1.22\lambda} = 51 m$