The smallest detail the human eye can resolve on the Moon depends on the diffraction limit, the wavelength of light, and the pupil diameter. While the formula for angular resolution can be applied, the exact size of the smallest detail resolvable isn't given without specific calculations. With an average pupil size and wavelength of light, a human eye under ideal conditions can distinguish features a few kilometers in size on the Moon's surface.
The smallest detail that the human eye can resolve on the Moon without a telescope relies on the diffraction limit of the human eye. According to the Rayleigh criterion, the angular resolution is determined by the wavelength of light (λ) and the diameter of the pupil (D) using the formula θ = 1.22 * (λ / D). Given that λ is approximately 550 nm for visible light and the average diameter of the human pupil is about 5 mm, we can calculate the angular resolution of the human eye.
However, to answer the given question of the smallest detail the eye can resolve on the Moon, we need not just angular resolution but also the actual size that corresponds to this angle at moon's distance.
Using 384,000 km as the distance to the Moon, we can estimate the physical size corresponding to the minimum angular resolution. However, without explicit figures from the provided context, we can generally say the human eye can resolve features on the Moon down to about a few kilometers in size under ideal observing conditions.