Question

Find the position of the object which when raised in front of convex mirror of focal length $20cm$ produces virtual image which is half size of the object.

Answer 1

The magnification is given as,

$m=-\frac{v}{u}$

$\frac{1}{2}=-\frac{v}{u}$

$\frac{1}{v}=-\frac{2}{u}$

The mirror formula is given as,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$-\frac{2}{u}+\frac{1}{u}=\frac{1}{20}$

$u=-20cm$

Thus, the position of the object is $-20cm$.