Question

An object is placed at a distance of 10 cm from a convex mirror of focal length 5 cm.

(i) Draw a ray-diagram showing the formation image
(ii) State two characteristics of the image formed
(iii) Calculate the distance of the image from mirror.

Answer 1

(i) Ray Diagram-

(ii) Following are the characteristics of the image formed:

(1) It is virtual and erect.
(2) It is smaller than the object.

(iii) Distance of the object 'u' = -10 cm
Focal length of the convex mirror is 5 cm.
We have to find the distance of the image 'v'.
Using the mirror formula, we get
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ \Rightarrow \frac{1}{5}=\frac{1}{v}+\frac{1}{-10} \\ \Rightarrow \frac{1}{5}=\frac{1}{v}-\frac{1}{10} \\ \Rightarrow \frac{1}{5}+\frac{1}{10}=\frac{1}{v} \\ \Rightarrow \frac{2}{10}+\frac{1}{10}=\frac{1}{v} \\ \Rightarrow \frac{1}{v}=\frac{3}{10} \\ \Rightarrow \mathrm{v}=\frac{10}{3}\Rightarrow \mathrm{v}=3.3\mathrm{cm} \end{gathered}$$
Thus, the distance of the image is 3.3 cm behind the mirror.