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 = ?`
`lambda = 5000 Å = 5 xx 10^(-5) cm`
Limit of resolution `d theta = (d)/(x) = (lambda)/(D)`
`:. D = (x lambda)/(D) = (10^(5) xx 5 xx 10^(-5))/(10) = 0.5 cm = 5 mm`