Question

A spherical mirror forms an image of size $3$ times that of the object. If the focal length of the mirror is $-24\text{cm}$, then the object distance may be:

• A. $18\text{cm}$ or $28\text{cm}$
• B. $18\text{cm}$ or $24\text{cm}$
• C. $32\text{cm}$ or $24\text{cm}$
• D. $32\text{cm}$ or $16\text{cm}$

Answer 1

The correct option is D $32\text{cm}$ or $16\text{cm}$

Given:
$f=-24\text{cm}$
As focal length is negative, the mirror is concave.
Here, the magnitude of magnification is $3$.
$|m|=3$
$\Rightarrow m=\pm 3$
$\Rightarrow m=\frac{f}{f-u}$
$\Rightarrow \pm 3=\frac{-24}{-24-u}$
$\Rightarrow -24-u=\pm 8$
$\Rightarrow u=-24\pm 8$
$\Rightarrow u=-16\text{cm}$ or $-32\text{cm}$
Hence, the distance of the object may be $32\text{cm}$ or $16\text{cm}$.

$\begin{array}{c}\text{Why this question?}\\ \text{The purpose of this question is to make you understand}\\ \text{that magnification produced by a concave mirror can be}\\ \text{positive or negative.}\end{array}$