Question

An object of size $10\text{cm}$ is placed at a distance of $30\text{cm}$ from a concave mirror of focal length $20\text{cm}$. The size of the image formed is -

• A. $10\text{cm}$
• B. $30\text{cm}$
• C. $20\text{cm}$
• D. $15\text{cm}$

Answer 1

The correct option is C $20\text{cm}$

Given:
$h_o=10\text{cm}$
$u=-30\text{cm}$
$f=-20\text{cm}$

Using mirror formula,

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

$\Rightarrow \frac{1}{(-20)}=\frac{1}{v}+\frac{1}{(-30)}$

$\Rightarrow v=-60\text{cm}$

Magnification for mirror is,

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

$\Rightarrow \frac{h_i}{10}=\frac{-(-60)}{(-30)}$

$\Rightarrow h_i=-20\text{cm}$

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