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  4. 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

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Q. 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

J & K CETJ & K CET 2014Ray Optics and Optical Instruments

Solution:

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}
$