Question

A converging mirror forms a real image of height 4 cm of an object of height 1 cm placed 20 cm away from the mirror:

(i) Calculate the image distance.
(ii) What is the focal length of the mirror?

Answer 1

A concave mirror is a converging mirror.

Distance of the object from the mirror 'u' = -20 cm

Height of the object 'h_o' = 1 cm

Height of the image 'h_i' = -4 cm
We have to find the distance of the image 'v' and focal length of the mirror 'f'.

Using the magnification formula, we get
$$\begin{gathered} m=\frac{h_i}{h_o}=-\frac{v}{u} \\ \frac{-4}{1}=\frac{-v}{-20} \\ v=\frac{20\times -4}{1}=-80\mathrm{cm} \end{gathered}$$

Thus, the distance of the image 'v' is 80 cm.

Now, using the mirror formula, we get

$$\begin{gathered} \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ \frac{1}{f}=\frac{1}{-80}+\frac{1}{-20}=-\frac{1}{80}-\frac{4}{80}=-\frac{5}{80} \\ \frac{1}{f}=-\frac{1}{16} \\ f=-16\mathrm{cm} \end{gathered}$$

Thus, the focal length of the concave mirror is 16 cm.