Light - Reflection and Refraction

Solution : 

Rules of sign convention:
1- Objects are always placed to the left of the mirror i.e. light must fall on the mirror from left to right.
2- All distances are measured from the pole of the mirror.
3- Distances along the direction of the incident ray are taken as positive, while distances along the direction of the reflected ray are taken as negative.
4- Heights measured perpendicular to and above the principal axis are taken as positive.
5- Heights measured perpendicular to and below the principal axis are taken as negative.

These sign conventions can also represented in the following diagram


Now, 
$$\begin{gathered} \mathrm{Object} \mathrm{distance}, \mathrm{u}=-16 \mathrm{cm} \\ \mathrm{Magnification}, \mathrm{m}=-\frac{\mathrm{v}}{\mathrm{u}}=3 \\ \mathrm{or} \mathrm{v}=-3\mathrm{u}=48 \mathrm{cm} \\ \mathrm{Now} \mathrm{using} \mathrm{mirror} \mathrm{formula}, \\ \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}} \\ =\frac{1}{48}+\frac{1}{(-16)}=\frac{1-3}{48}=-\frac{2}{48}=-\frac{1}{24} \\ \mathrm{or} \mathrm{f}=-24 \mathrm{cm} \end{gathered}$$