Question

The distance between an object and its double magnified image formed by a concave mirror of focal length $f$ is

• A. $\frac{3f}{2}$
• B. $\frac{2f}{3}$
• C. $3f$
• D. Depends on whether the image is real or virtual.

Answer 1

The correct option is A $\frac{3f}{2}$

Given, Magnification $m=2$

Case $\left(I\right):$ For $m=2$

$m=-\frac{v}{u}=2$

$\Rightarrow v=-2u$

Using mirror formula,

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

$\Rightarrow \frac{1}{f}=\frac{1}{-2u}+\frac{1}{u}$

$\Rightarrow \frac{1}{f}=\frac{1}{2u}$

$\Rightarrow u=\frac{f}{2}$

$\therefore v=-f$

Distance between object and image

$\left|d\right|=u-v=\frac{f}{2}+f=\frac{3f}{2}$

Case $\left(II\right):$ For, $m=-2$

$m=-\frac{v}{u}=-2$

$\Rightarrow v=2u$

$\Rightarrow \frac{1}{f}=\frac{1}{2u}+\frac{1}{u}$

$\Rightarrow u=\frac{3f}{2}\text{and}v=3f$

The distance between object and image

$\left|d\right|=|u-v|=3f-\frac{3f}{2}=\frac{3f}{2}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.