Question

The next generation of large telescopes includes a proposed 30 m telescope on top of Mauna Kea in Hawaii. If this telescope is pointed towards two identical stars which orbit around each other at the Neptune-Sun distance of 4.5 billion km = 4.5 × 10^12m, what is the maximum distance in meters between Earth and the two stars at which the telescope can still resolve them? Assume that the telescope observes light with a wavelength of 500 nm.

The answer is 2.2 × 10^20 meters, but I do not understand how to get that answer. I tried using sintheta= 1.22(lambda/d) but did not come up with the right answer.

Answer 1