Question

The radius of curvature of a convex mirror is $60\text{cm}$. When an object is placed at $B$ its image is formed at $B^{\prime }$. If size of the image is half that of the object then the distance between $B$ and $B^{\prime }$ is

• A. $30\text{cm}$
• B. $60\text{cm}$
• C. $45\text{cm}$
• D. $90\text{cm}$

Answer 1

The correct option is C $45\text{cm}$

Given:
$R=60\text{cm}$
So, $f=\frac{R}{2}=+30\text{cm}$
$m=\frac{+1}{2}$
Now, $m=\frac{f}{f-u}$
$\Rightarrow \frac{+1}{2}=\frac{+30}{+30-u}$
On solving this, we get,
$u=-30\text{cm}$
Similarly,
$m=\frac{-v}{u}$
$\Rightarrow \frac{+1}{2}=\frac{-v}{-30}$
On solving this, we get,
$v=+15\text{cm}$
Image is formed behind the mirror while the object is in front of the mirror. Hence distance $=u+v$
Therefore, distance between $B$ and $B^{{}^{\prime }}=|u|+|v|=30+15=45\text{cm}$