Question

A convex mirror is placed in the path of the converging rays at a distance of $30\text{cm}$ infront of the point of convergence. If the reflected rays appear to diverge from a point $1.2\text{m}$ from the mirror, find its focal length.

• A. $16\text{cm}$
• B. $-20\text{cm}$
• C. $24\text{cm}$
• D. $-30\text{cm}$

Answer 1

The correct option is C $24\text{cm}$


Here the object and image both are virtual.
Taking direction of incident light as +ve,
Object distance, $u=+30\text{cm}$
and image distance, $v=+1.2\text{m}=+120\text{cm}$
Using mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{120}+\frac{1}{30}=\frac{1}{f}$
$\Rightarrow \frac{1+4}{120}=\frac{1}{f}$
$\therefore f=\frac{120}{5}=24\text{cm}$
Thus, focal length is $+24\text{cm}$