Final answer:
The minimum diameter mirror on a telescope that would allow you to see details as small as 5.00 km on the Moon some 384,000 km away is approximately 1.50 meters. Therefore, the correct answer is (c) 1.5 m.
Step-by-step explanation:
To determine the minimum diameter mirror on a telescope that would allow you to see details as small as 5.00 km on the Moon, we can use the concept of diffraction limit.
According to the Rayleigh criterion, the minimum angular resolution of a telescope is determined by the formula θ = 1.22 * λ / D, where θ is the angular resolution, λ is the wavelength of light, and D is the diameter of the mirror. Rearranging the formula to solve for D, we get D = 1.22 * λ / θ. Plugging in the values, we have λ = 550 nm and θ = 5.00 km / 384,000 km.
Converting km to meters, θ becomes 5.00 * 10^3 m / 3.84 * 10^8 m. Substituting these values into the formula, we can calculate the minimum diameter of the mirror on the telescope.
Minimum diameter of the mirror = 1.22 * (550 nm) / (5.00 * 10^3 m / 3.84 * 10^8 m)
After evaluating the expression, we find that the minimum diameter of the mirror on the telescope is approximately 1.50 meters. Therefore, the correct answer is (c) 1.5 m.