Question

A convex mirror of radius of curvature 20 cm forms an image which is half the size of the object.How far is the object from the mirror ?

• A. 5 cm
• B. 7.5 cm
• C. -30 cm
• D. 12.5 cm

Answer 1

The correct option is C -30 cm

Radius of curvature $=20cm$

So$,$ focal length $=10cm$

We are given$,$ $h_o/2=h_i$

$so,h_o=2h_i$

$so,m=h_i=h_o$

$m=h_o/2h_o$

$so,m=-v/u$

$1/2=-v/u$

$so,u=-2v$

By mirror formula$,$

$1/f=1/v+1/u$

$1/10=1/v-\left(-1/2v\right)$

$1/10=1/v+1/2v$

$so,1/10=2+1/2v$

$so,1/10=3/2v$

$so,2v=30$

$so,v=15cm$

$u=-2\left(v\right)=-30$

Hence,

option $\left(C\right)$ is correct answer.