Question

A concave mirror of focal length $f$ produces an image $n$ times the size of the object. If image is real then the distance of object from the pole of 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 C $\left[\frac{(n+1)}{n}\right]f$

Given, the image is real and its size is $n$ times the size of the object.

$\therefore$ magnification $\left(m\right)=-n$

And from magnification formula,

$m=\frac{f}{f-u}$

taking sign convention for concave mirror and substituting the value of magnification we get,

$-n=\frac{-f}{-f-u}\Rightarrow u=-\frac{f(n+1)}{n}$

So, the distance of the object from mirror is $\frac{(n+1)f}{n}$

Hence, option (c) is the correct answer.