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

Answer

C

Explanation

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