Question

A telescope has an objective of diameter of 60 cm. The focal lengths of the objective and eye piece are 2.0 m and 1.0 cm respectively. The telescope is directed to view two distant almost point sources of light (e.g. two stars of a binary). The sources are at roughly the same distance (= 10⁴ light years) along the line of sight but separated transverse to the line of sight by a distance of 10¹⁰ m. Will the telescope resolve the two objects i.e. will it see two distinct stars?

Answer 1

Distance between two stars, d = 10¹⁰ m

Distance of stars from objective,

D = 10⁴ light years

= 10⁴ x 10¹⁶ m (∵ 1 light year ≃ 10¹⁶ m)

Objective diameter (aperture),

a = 60 cm = 0.60 m

Wavelength of light used,

λ = 5500 x 10^-8 m

Angle subtended by the stars on the telescope; objective.

\(\frac{d}{D} = \frac{10^{10}}{10^{20}}\) = 10^-10 radians

Limit of angular resolution of telescope objective,

dθ = \(\frac{1.22 \lambda}{a}\)

= \(\frac{1.22 \times 5500 \times 10^{-8}}{0.60}\)

= 1.118 x 10^-6 radians