Answer:
The minimum angular separation between the two stars to be resolved is [tex]8.13x10^{-6}rad[/tex].
Explanation:
A star looks like a point in the celestial sphere since it is at a great distance. However, the resulting image in a telescope that will get from the star is a diffraction pattern instead of a perfect point (point spread function (PSF)).
That can be understood as that the image is a blur around the central point. In which 84% of the energy is in the central source of the diffraction pattern.
That diffraction pattern is getting because the light encounters different obstacles on its path inside the telescope (interact with the walls and edges of the instrument).
The diffraction pattern is composed of a central disk, called Airy disk, and diffraction rings.
The angular resolution is defined as the minimal separation at which two sources can be resolved one of another, or in other words when the distance between the two diffraction pattern maxima is greater than the radius of the Airy disk.
The angular resolution can be determined as an analytical way by means of the Rayleigh criterion.
[tex]\theta = 1.22\frac{\lambda}{D}[/tex] (1)
Where [tex]\lambda[/tex] is wavelength and D is the diameter of telescope.
Notice that it is necessary to express the diameter and the wavelength in the same units.
[tex]\lambda = 400nm \cdot \frac{1x10^{-9}m}{1nm}[/tex] ⇒ [tex]4x10^{-7}m[/tex]
[tex]D = 60.0mm \cdot \frac{1m}{1000nm}[/tex] ⇒ [tex]0.06m[/tex]
Finally, equation 1 can be used.
[tex]\theta = 1.22(\frac{4x10^{-7}m}{0.06m})[/tex]
[tex]\theta = 8.13x10^{-6}rad[/tex]
Hence, the minimum angular separation between the two stars to be resolved is [tex]8.13x10^{-6}rad[/tex].
