Question

An object $1cm$ tall is placed infront of a mirror at a distance of $4cm$. In order to produce an upright image of $3cm$ height one needs a

• A. convex mirror of radius of curvature $12cm$
• B. concave mirror of radius of curvature $12cm$
• C. concave mirror of radius of curvature $4cm$
• D. plane mirror of height $12cm$

Answer 1

The correct option is B concave mirror of radius of curvature $12cm$

Given
Object distance $u=-4cm$
Size of object $O=+1cm$
Size of Image $I=+3cm$
Magnification $m=\frac{I}{O}=\frac{f}{f-u}$
Here $f$ is focal length of the mirror
$\frac{I}{O}=\frac{f}{f-u}\Rightarrow \frac{+3}{+1}=\frac{f}{f-(-4)}$
$\Rightarrow f=-6cm$
($-ve$ sign of focal length indicates concave mirror)
$\Rightarrow$Radius of curvature $R=2f=12cm$
$\therefore$ Erect and enlarged image of size $3cm$ can be produced by concave mirror of radius of curvature $12cm$