A binary star system in the constellation orion has an angular separation of 10-5 rad. if the wavelength of the light from the system is 500 nm, what is the smallest aperture (diameter) telescope that can just resolve two stars?

The answer is: Diameter = d = 6.1 cm

Explanation:

Angular separation between the two stars = Q = 10^-5 rad.

Wavelength = λ = 500 * 10^-9 m

The smallest diameter = d = ?

As Q = 1.22 * (λ / d)

From this

d = 1.22 * (λ/Q) - - - (1)

Plug in the value in (1):

(1) = > d = 1.22 * ((500*10^-9) / 10^-5))

d = 0.061 m

d = 6.1 cm