Question

(a) Draw a ray 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) Image

(b) $$h_{1}=1cm$$, u=-30cm,f=20cm, $$h_{2}=?$$, v=?

$$\displaystyle \frac{1}{v}+\frac{1}{u}=\frac{1}{f}$$

$$\displaystyle \Rightarrow \frac{1}{v}+\frac{1}{\left

(-30 \right )}=\frac{1}{20}$$

$$\displaystyle \Rightarrow

\frac{1}{v}=\frac{1}{30}+\frac{1}{20}$$

$$\therefore v=12 cm$$

The image is formed 12cm behind the mirror.

$$m=-\dfrac{v}{u}=\dfrac{h_{2}}{h_{1}}$$

$$ m=-\frac{12}{-30}=\frac{h_{2}}{1}$$

$$h_{2}=0.4cm$$