Question

(a) Draw a diagram to represent a convex mirror. On this diagram mark principal axis, principal focus F and the centre of curvature C if the focal length of convex mirror is 3 cm.
(b) An object 1 cm tall is placed 30 cm in front of a convex mirror of focal length 20 cm. Find the size and position of the image formed by the convex mirror.

Answer 1

(a) Ray Diagram-

(b) Given,
The mirror is a diverging mirror, i.e. convex mirror.

Height of the object 'h_o' = 1 cm

Distance of the object from the mirror 'u' = -30 cm

Focal length of the convex mirror 'f' = 20 cm

We have to find the position of the image 'v', height of the image 'h_i' and its magnification 'm'.

Using the mirror formula, we get
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ \Rightarrow \frac{1}{20}=\frac{1}{v}+\frac{1}{-30} \\ \Rightarrow \frac{1}{30}+\frac{1}{20}=\frac{1}{v} \\ \Rightarrow \frac{2}{60}+\frac{3}{60}=\frac{1}{v} \\ \Rightarrow \frac{5}{60}=\frac{1}{v} \\ \Rightarrow v=\frac{60}{5}=12\mathrm{cm} \end{gathered}$$

The image will be at a distance of 12 cm behind the mirror .

Now, using the magnification formula, we get

$$\begin{gathered} m=\frac{-v}{u} \\ m=\frac{-12}{-30}=0.4 \end{gathered}$$

Thus, the image is virtual, erect and smaller in size.

Also,

$$\begin{gathered} m=\frac{h_i}{h_o} \\ \Rightarrow 0.4=\frac{h_i}{1} \\ \Rightarrow h_i=0.4\mathrm{cm} \end{gathered}$$

Therefore, the height of the image is 0.4 cm.