Question

A telescope has an objective lens of focal length $200\text{cm}$ and an eyepiece with focal length $2\text{cm}$. If this telescope is used to see a $50\text{m}$ tall building at a distance of $2\text{km}$, what is the height of the image of the building formed by the objective lens ?

• A. $5\text{km}$
• B. $5\text{m}$
• C. $5\text{cm}$
• D. $1\text{m}$

Answer 1

The correct option is C $5\text{cm}$

Given,
Focal length of objective lens, $f_0=200\text{cm}$

Focal length of eye-piece, $f_e=2\text{cm}$

Height of building, $h=50\text{m}$ and its distance is $2\text{km}$.


Since, the object distance is very large compared to focal length of the objective lens. So, the image of the building will form near the focal length of the objective.

$\therefore h_0=50\text{m},u=-2\text{km}=-2000\text{m}$

$v=f_0=200\text{cm}=2\text{m}$

Let the height of the image be $h_i$.

Now, we know magnification, $m=\frac{v}{u}=\frac{h_i}{h_0}$

$\Rightarrow \frac{2}{-2000}=\frac{h_i}{50}$

$\therefore h_i=-\frac{1}{20}\text{m}=-5\text{cm}$

Hence, $\left(\text{C}\right)$ is the correct answer.

Key point: Whenever object distance is large compared to focal length of the lenses, the object is considered to be at infinity.