Question

a concex mirror of focal length f produces an image (1 upon n)th of the size of the object . the distance of the object from the mirror is??

Answer 1

Final Answer :| u | = f(1-n)

Understanding :
1) magnification, m. = -v/u = h(i)/h(o)
where symbols have usual meaning

2) Mirror equation,
$\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$
where symbols have usual meaning.

Steps :
1) We know
magnification,
$m = \frac{1}{n} = \frac{ - v}{u} \\ = > \frac{ - u}{v} = n \: \: \: - - - - (1)$
2) Using Mirror Equation,
$\frac{1}{u} + \frac{1}{v} = \frac{1}{f} \\ = > 1 + \frac{u}{v} = \frac{u}{f} \\ = > 1 - n = \frac{u}{f} \\ = > u = f(1 - n)$


4) Object distance,
$|u| = |f(1 - n)|$