Question

the distance of an object from a concave mirror of focal length 12cm for the magnification of 4 shall be

Answer 1

given:. u=?
f=12cm
m=4

$m = \frac{ - v}{u}$
$4 = \frac{ - v}{u}$
$4u = - v$
$u = \frac{ - v}{4}$
But the sign of v is not substituted in the above formula because u is in terms of v.
Therefore as object distance is measured opposite to the incident ray,
$u = - ( \frac{ - v}{4} ) = \frac{v}{4}$
we know that
$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
$\frac{1}{12} = \frac{1}{ \frac{v}{4} } + \frac{1}{v}$
$\frac{1}{12} = \frac{4}{v} + \frac{1}{v}$
$\frac{1}{12} = \frac{5}{v}$
$v = 60cm$
$u = \frac{v}{4}$
$u = \frac{60}{4}$
$u = 15cm$