Question

A telescope has an objective lens of focal length $200cm$ and an eyepiece with focal length $2cm$. It is used to see a $50m$ tall building at a distance of $2km$. What is the height of the image of building formed by the objective lens?

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

Answer 1

Answer: (A)

$5cm$

We have,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$⟹\frac{1}{v}=\frac{1}{200}-\frac{1}{2000\times 100}$

$⟹v=200cm$

We have $\frac{v}{u}=\frac{I}{O}$

$⟹I=\frac{2}{2000}\times 50$

$⟹I=\frac{1}{20}m=5cm$