A telescope has an objective lens of `10cm` diameter and is situated at a distance of one kilometre from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is `5000 Å`, of the order of

Options

A. 5 mm
B. 5 cm
C. 2.5 m
D. 5 m

Answer

A

Explanation

Here, `D = 10 cm, x = 1 km = 10^5 cm`
Distance between two objects, `d = ?`
`lamda = 5000 Å = 5 xx 10^-5 cm`
Limit of resolution `d theta = (d)/(x) = (lamda)/(D)`
`:. d = (x lamda)/(D) = (10^5 xx 5 xx 10^-5)/(10) = 0.5 cm = 5 mm`.