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
​

Answer 1

Answer: The distance of the object from the mirror is :$\frac{f(n+1)}{n}$

Explanation: So, it's given that the mirror is concave.

∴ By Cartesian Sign Convention,

Focal Length = (-f)

Image Distance = (-v) [∵ image formed is real]

Object Distance = (-u)

Magnification = -n

Now,

Using Mirror Formula,

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

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

⇒$\frac{-1}{v} = \frac{f-u}{fu}$

⇒$\frac{1}{v} = \frac{u-f}{fu}$

⇒ $v = \frac{fu}{u-f}$

We know,

Magnification = (-n)

⇒ (-n) = $\frac{-v}{u}$

⇒ $(-n) = \frac{\frac{-fu}{u-f} }{u}$  [putting value of 'v' obtained earlier]

⇒$n=\frac{\frac{fu}{u-f} }{u}$

⇒$n= f/(u-f)$

⇒nu - nf = f

⇒nu = f + nf

⇒u = $\frac{f(n+1)}{n}$ , which is your answer :)