Final answer:
The Gemini North telescope can resolve objects on the moon that are at least 36.5 meters apart using diffraction effects.
Step-by-step explanation:
To determine how far apart two objects on the moon must be to be resolvable by the 8.1-m-diameter Gemini North telescope, we can use the formula for the angular resolution of a telescope, which is given by:
θ = 1.22 * (λ / D)
Where θ is the angular resolution in radians, λ is the wavelength of light, and D is the diameter of the telescope's aperture.
Given that the wavelength of light is 550 nm (or 550 * 10^-9 meters) and the diameter of the Gemini North telescope is 8.1 meters, we can substitute these values into the equation:
θ = 1.22 * (550 * 10^-9 / 8.1)
Calculating the result gives us an angular resolution of approximately 9.14 * 10^-8 radians.
To find the distance between the two objects on the moon that correspond to this angular resolution, we can use the formula:
d = R * θ
Where d is the distance between the objects, R is the distance to the moon (400,000 km), and θ is the angular resolution. Substituting the values:
d = 400,000 km * 9.14 * 10^-8
Calculating the result gives us a distance of approximately 0.0365 km, or 36.5 meters. Therefore, two objects on the moon must be at least 36.5 meters apart to be resolvable by the Gemini North telescope.