Question

A concave mirror of focal length $f$ produced an image $m$ times the size of the objects. If the image is real, then what is the distance of the object from the mirror?

Answer 1

Given,

Magnification, $M=m$

Focal length, $F=f$

Image is real, so $M=-m$, as the image will be inverted.

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

$\Rightarrow$ $v=um$

From mirror formula,

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

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

$\Rightarrow$ $f=\frac{um}{1+m}$

$\Rightarrow$ $u=(1+m)\frac{f}{m}\to$ Object distance