A telescope has an objective lens of focal length `200cm` and an eye piece with focal length `2cm`. If this telescope is used to see a 50 meter tall building at a distance of `2km,` what is the height of the image of the building formed by the objective lens?

Options

A. 5 cm
B. 10 cm
C. 1 cm
D. 2 cm

Answer

A

Explanation

From the formula for convex lens,
`(1)/(v)-(1)/(u)=(1)/(f)`
`therefore" "v=(fxxu)/(u-f)=(200xx200xx10^(3))/([200xx10^(3)-200])=(200xx10^(3))/(999)`
Also, magnification,
`m=|(v)/(u)|=|(t)/(O)|`
`=(200xx10^(3))/(999xx200xx10^(3))=(I)/(50xx100)`
`I=(5000)/(999) cong 5 cm`.