Question

Two stars 19 light-years away are barely resolved by a 63 cm (mirror diameter) telescope. 1ly=9. 461×1015m. How far apart are the stars? Assume λ = 550 nm and that the resolution is limited by diffraction.

d=_____? m

Answer 1

θ = sin^-1 (1.22 × 550 × 10^-9 m / 0.63 m)

θ ≈ 1.59 × 10^-6 rad

d = sin (1.59 × 10^-6 rad) × (19 × 9.461 × 10^15 m)

d ≈ 5.6 × 10^12 m

Therefore, the stars are approximately 5.6 × 10^12 m or 5.6 trillion kilometers apart.