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. 0.5 m
B. 5 m
C. 5 mm
D. 5 cm

Answer

C

Explanation

Given, `lambda=5000 "Å"=5000xx10^(-10)m`,
D=1km=1000m,
and d=10 cm=0.1m
Resolving limit of telescope
`theta prop (x)/(D)=(lambda)/(D) rArr x=(lambdaD)/(d)`
`therefore x=(5000 xx 10^(-10)xx1000)/(0.1)`
`=5xx10^(-3)m=5mm`