Question

At what distance in front of a concave mirror of focal length $10$cm, an object be placed so that its real image of size five times that of the object obtain?

Answer 1

$f=10$cm.
We know that, linear
magnification
$m=\frac{I}{O}$
$I=$ size of image
$O=$ size of object
But, here the real image is 50 times of object.
$I=50$
$m=\frac{50}{0}=m=-5$
By the definition of linear magnification
$m=\frac{f-u}{f}$
$5=\frac{10-u}{10}$
$50=10-u$
$u=40$
$u=40$cm.
Object should be placed at $40$cm in front of convex mirror. Here $-$ve sign represents that object is placed left side of the mirror.