(a) For which position of an object, a concave mirror forms a real image equal in size to the object?
(b) State one use of a concave mirror.
(c) An object of height 1 cm is placed at a distance of 15 cm from a concave mirror of radius of curvature 20 cm. Find the position, nature and size of the image formed.

(a) When the object is placed at the radius of curvature of a concave mirror, then the image formed is equal in size with the object.

(b) Concave mirrors are used in motor vehicle headlights to reflect strong beams of light.

(c) Radius of curvature of the lens = 20 cm

Focal length = 10 cm

Object distance = 15 cm

Using mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$$\begin{gathered} \Rightarrow \frac{1}{v}=\frac{1}{-10}-\frac{1}{-15}=-\frac{1}{30} \\ \Rightarrow v=30\mathrm{cm} \end{gathered}$$

Magnification of the mirror is given by the relation,

$$\begin{gathered} m=-\frac{v}{u}=-\frac{30}{15}=-2 \\ \Rightarrow m=-2=\frac{h_{\mathrm{i}}}{h_{\mathrm{o}}} \\ \Rightarrow h_{\mathrm{i}}=-2h_{\mathrm{o}}=-2\times 1\mathrm{cm}=-2\mathrm{cm} \\ \Rightarrow {\mathrm{h}}_{\mathrm{i}}=-2\mathrm{cm} \end{gathered}$$

Nature of the image is virtual, inverted and enlarged.