Question

A concave mirror of focal length $f$ produces an image $n$ times the size of the object. If the image is real, then the distance of the object from the mirror is :

• A. $(n-1)f$
• B. $\left(\frac{n+1}{n}\right)f$
• C. $\left(\frac{n-1}{n}\right)f$
• D. $(n+1)f$

Answer 1

The correct option is B $\left(\frac{n+1}{n}\right)f$

Given:
Focal length of the mirror $=f$
The size of the image is $n$ times the size of the object.
So, magnification, $m=-n$
$[$image is real$]$
Also, $m=-\frac{v}{u}$
$\Rightarrow m=\frac{f}{f-u}$ $(\because v=\frac{uf}{u-f})$
$\Rightarrow -n=\frac{-f}{-f-(-u)}$
$[$as per sign convention for concave mirror$]$
$\Rightarrow -n=\frac{-f}{-f+u}$
$\Rightarrow nf-nu=-f$
$\Rightarrow f(n+1)=nu$
$\Rightarrow u=\frac{f(n+1)}{n}$
Thus, the distance of the object from the mirror is $\frac{f(n+1)}{n}$