Question

At what distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?

Answer 1

We know $magnification=\frac{heightoftheobject}{heightoftheimage}$

Also, $magnification=\frac{-imagedistance}{objectdistance}$

$-\frac{V}{U}=\frac{h_i}{h_0}=\frac{6}{2}=3$

$-V=3U$

From, $\frac{1}{f}=\frac{1}{V}-\frac{1}{U}$

$\frac{-1}{10}=\frac{1}{-3U}+\frac{1}{U}$

$\frac{-1}{10}=\frac{2}{3U}⟹-10=\frac{3U}{2}⟹U=\frac{-20}{3}=6.7m$