Question

Find the position and nature of the image formed by the concave mirror of focal length $20\text{cm}$, if the object $\text{O}$ is placed at a distance of $30\text{cm}$ from the mirror.

• A. $60\text{cm}$ , Virtual image
• B. $30\text{cm}$ , Real image
• C. $60\text{cm}$ , Real image
• D. $30\text{cm}$ , Virtual image

Answer 1

The correct option is C $60\text{cm}$ , Real image

For a concave mirror, $u$ and$f$ are negative.
[$u$ is negative for a real object]

Given,

Focal length of the concave mirror $f=-20\text{cm}$

Object distance, $u=-30\text{cm}$


$\therefore$ Image distance is given by
$v=\frac{uf}{u-f}[\because \frac{1}{f}=\frac{1}{u}+\frac{1}{v}]$

Substituting the given data, we get

$v=\frac{(-20)(-30)}{-30+20}=-60\text{cm}$

Since $v$ is negative, the image formed is real.

Hence, option (c) is the correct answer.

Note:- For a concave mirror, as far as $u>f$, we can say that $u$ , $v$ and $f$ are all negative.