A telescope has an objective of diameter 60 cm.The focal lengths of the objective and eyepiece 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 year) along the line of sight but are separated transverse to the line of sight by a distance of `10^10` m. Will the telescope resolve the two objects i.e. will it see two distant stars?

Explanation

Data on focal lengths is not required. The limit of resolution of the telescope is given by
`theta = (1.22 lamda)/(D) = (1.22 xx 6 xx 10^(-7))/(0.60) rad = 1.22 xx 10^(-6) rad`
Here, the value of chosen corresponds roughly to the wavelength of yellow light. The transverse separation between the two sources subtends an angle equal to
` (10^10 m)/( 9.46 xx 10^19 m) ~~ 10^(-10) rad`
Here, we have used 1 light year `= 9.46 xx 10^15 m `This angle is much too small compared to `theta` above. The two stars of the binary cannot be resolved by the given telescope.