Question

A concave mirror, having focal length of $15\, cm$, forms an image having twice of the linear dimensions of the object. If the image is virtual, then the position of the object will be

• A. 7.5 cm
• B. 22.5 cm
• C. 40 cm
• D. 30 cm

Answer 1

Answer: (A)

Image formation by concave mirror will be as follows:

Given, $m=\frac{\text { image distance }}{\text { object distance }}=-\frac{v}{u}=2$
$\Rightarrow v=-2 u$
Also $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
where $f$ is focal length, $v$ is image distance and $u$ is object distance.
$ \Rightarrow-\frac{1}{15}=\frac{1}{u}-\frac{1}{2 u}=\frac{1}{2 u} $
$ \Rightarrow u=-\frac{15}{2}=-7.5 \,cm$
Thus, the object should be placed at a distance $7.5 \,cm$ in front of the mirror.