Question

A concave mirror of focal length $f$ produces a real image $n$ times the size of the object. The distance of the object from the mirror is

• A. $(n-1)f$
• B. $(n+1)f$
• C. $(n+1)f/n$
• D. $(n-1)f/n$

Answer 1

Answer: (C)

$(n+1)f/n$

Answer 2

Since the image is real, it must be inverted and magnification ratio should be negative.
Mgnification $=\frac{- v }{ u }$
$- n =\frac{- v }{ d }, u = d$ is the distance of object and and image distance is $v$
$v = nd$
Now using mirror formula
$\begin{array}{l} \frac{1}{ f }=\frac{1}{ v }+\frac{1}{ u } \\\ \frac{1}{ f }=\frac{1}{ nd }+\frac{1}{ d } \\\ \text { So } d =\frac{ f ( n +1)}{ n } \end{array}$