Final answer:
The minimum angular separation of two stars just-resolvable by the 8.1-m Gemini South telescope is determined using the diffraction limit formula for a circular aperture, considering the wavelength of light as 550 nm and the telescope's diameter as 8.1 meters.
Step-by-step explanation:
The minimum angular separation of two stars that are just-resolvable by the 8.1-m Gemini South telescope can be calculated using the diffraction limit formula for a circular aperture:
\(\theta = 1.22 \frac{\lambda}{D}\)
Where \(\theta\) is the angular resolution in radians, \(\lambda\) is the wavelength of light, and D is the diameter of the telescope's aperture.
Given that the wavelength \(\lambda\) is 550 nm (which is \(550 \times 10^{-9}\) meters) and the diameter D of the Gemini South telescope is 8.1 meters, we can substitute these values into the formula:
\(\theta = 1.22 \frac{550 \times 10^{-9}}{8.1}\)
After calculation, we obtain \(\theta\), which is the minimum angular separation for the Gemini South telescope to just resolve two stars, assuming no atmospheric effects are limiting resolution.