Question

A concave mirror has a focal length of $20\text{cm}$. The distance between two possible positions of the object for which the image size is double of the object size is

• A. $40\text{cm}$
• B. $20\text{cm}$
• C. $30\text{cm}$
• D. $60\text{cm}$

Answer 1

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

Given:
$f=-20\text{cm}$
Here, the magnitude of magnification is $2$.
$|m|=2$
$\Rightarrow m=\pm 2$
$\Rightarrow m=\frac{f}{f-u}$
$\Rightarrow \pm 2=\frac{-20}{-20-u}$
$\Rightarrow -20-u=\pm 10$
$\Rightarrow u=-20\pm 10$
$\Rightarrow u=-10\text{cm}$ or $-30\text{cm}$
Hence, the distance of the object may be $30\text{cm}$ or $10\text{cm}$.
So, the distance between the two positions of the object $=30-10=20\text{cm}$

$\begin{array}{c}\text{Why this question?}\\ \text{Magnification is possible for both real and virtual images.}\end{array}$