Question

Two stars 15 light-years away are barely resolved by a 69 −cm (mirror diameter) telescope. How far apart are the stars? Assume λ=560nm and that the resolution is limited by diffraction. Express your answer using two significant figures.

Answer 1

The Rayleigh criterion for a minimum resolvable angle gives the angular resolution of any circular aperture to be

Sometimes approximation is also used.

Using we get

Let d be the separation between the two stars that are barely resolved. Using

Using we get,

If we had used the approximation instead