Question

A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm. The image will form at
(a) infinity
(b) pole
(c) focus
(d) 15 cm behind the mirror.

Answer 1

(d) 15 cm behind the mirror

Since u = − 30 cm
v = ?
f = 30 cm

From the mirror formula:
$$\begin{gathered} \frac{1}{u}+\frac{1}{v}=\frac{1}{f} \\ \mathrm{or}\frac{1}{v}=\frac{1}{f}-\frac{1}{u} \\ \Rightarrow \frac{1}{v}=\frac{1}{30}-\frac{1}{-30} \\ \frac{1}{v}=\frac{1}{30}+\frac{1}{30} \\ \frac{1}{v}=\frac{2}{30} \\ \therefore v=15\mathrm{cm} \end{gathered}$$