Question

An object is placed at $60\text{cm}$ in front of a convex lens of focal length $40\text{cm}$. What will be the height of the image if the object is $5\text{cm}$ high?

• A. $15\text{cm}$
• B. $13\text{cm}$
• C. $10\text{cm}$
• D. $17\text{cm}$

Answer 1

The correct option is C $10\text{cm}$

Given :
Object distance, $u=-60\text{cm}$
Focal length, $f=40\text{cm}$
Object height, $h_o=5\text{cm}$

Using lens formula,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\Rightarrow \frac{1}{40}=\frac{1}{v}-\frac{1}{(-60)}$

$\Rightarrow v=120\text{cm}$

Now, magnification,

$m=\frac{v}{u}=\frac{h_i}{h_o}$

$\Rightarrow \frac{120}{-60}=\frac{h_i}{5}$

$\Rightarrow h_i=-10\text{cm}$

Hence, option $\left(C\right)$ is the correct answer.