A telescope has an objective of diameter `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 roughly at the same distance (`10^(4)` light years) along the line of sight, but separated transverse to the line of sight by a distance of `10^(10)m`. Will the telescope resolve the two objects ?

Explanation

Here, `D = 60 cm = 0.6 m`,
`f_(0) = 2.0 n, f_(e) = 1.0 cm`,
Distance between stars `= 10^(4)` light years
`= 10^(4) xx (9.46 xx 10^(15)m) = 9.46 xx 10^(19)m`
Transverse separation of stras `= 10^(10)m`.
Angle subtended by transverse separation of stras `= (10^(10))/(9.46 xx 10^(19)) ~~ 10^(-10) radian`
Smallest angular separation between two objects that can be resolved by the telescope = limit of resolution of telescope.
`d theta = (1.22 lambda)/(D) = (1.22 xx (6 xx 10^(-7)))/(0.6)`
` = 1.22 xx 10^(-6) rad`.
(Here, `lambda = 6 xx 10^(-7)m` for mean yellow colour)
As the angle subtended by transverse separation of stars is much too small compared to limit of resolution of telescope, therefore, the two stras of the binary cannot be resolved by the telescope.