Final answer:
The smallest detail that a reasonable quality telescope can resolve on the Moon is determined by the diffraction limit, considering the telescope's aperture and the wavelength of light. For the Hubble Space Telescope with an angular resolution of 0.1 arcseconds, the smallest detail it could resolve on the Moon would be around 185 meters.
Step-by-step explanation:
The smallest detail that a reasonable quality telescope can resolve on the Moon is determined by its diffraction limit, which is a function of the telescope's aperture (mirror diameter) and the wavelength of light used for observing. The diffraction limit is given by the formula Δθ = 1.22 λ / D, where Δθ is the angular resolution, λ is the wavelength of light, and D is the diameter of the telescope's mirror.
To calculate the physical size of the smallest detail that can be resolved on the Moon, we can multiply the angular resolution by the distance to the Moon. For example, if the Hubble Space Telescope has an angular resolution of about 0.1 arcseconds (which is a reasonable quality for ground-based telescopes as well), and the Moon is approximately 384,000 km away, we would use the small angle approximation formula s = θd, where s is the size of the detail, θ is the angular size in radians, and d is the distance to the Moon.