Question

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

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

Answer 1

The correct option is A 5 cm

Given, $u=-2000m,v=?,f=200cm=2m$

From lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}+\frac{1}{2000}=\frac{1}{2}$

$\frac{1}{v}=\frac{1}{2}-\frac{1}{2000}=\frac{1000-1}{2000}=\frac{999}{2000}$

$v=\frac{2000}{999}$

Magnification, $\frac{v}{u}=m=\frac{2000}{999\times 2000}=\frac{1}{999}$

Size of image $=\frac{1}{999}\times 50\times 100cm\approx 5cm$