Question

A mirror produces a virtual image four times enlarged of a boy standing $2.5\text{m}$ away from it. The type of mirror and its radius of curvature will be

• A. Convex, $3.33\text{m}$
• B. Convex, $6.67\text{m}$
• C. Concave, $3.33\text{m}$
• D. Concave, $6.67\text{m}$

Answer 1

The correct option is D Concave, $6.67\text{m}$

Given:
$m=+4$
$[$the image is virtual$]$
$u=-2.5\text{m}$
So, $m=\frac{f}{f-u}$
$\Rightarrow +4=\frac{f}{f-(-2.5)}$
On solving this, we get,
$f=-3.33\text{m}$
As focal length is negative, the mirror is concave.
Now, radius of curvature of the mirror,
$|R|=2|f|=6.67\text{m}$