Question

A 3 cm tall object is placed at a distance of 7.5 cm from a convex mirror of focal length 6 cm. Find the location, size and nature of the image.

Answer 1

Given,
Height of the object AB, h₁ = 3 cm
Distance of the object from the convex mirror, u = −7.5 cm
Focal length of the convex mirror (f) = 6 cm
Using mirror formula,
$$\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u} \end{gathered}$$
Putting values according to sign convention,
$$\begin{gathered} \frac{1}{v}=\frac{1}{6}-\frac{1}{(-7.5)} \\ \frac{1}{v}=\frac{1}{6}+\frac{1}{7.5}=\frac{3}{10} \\ \Rightarrow v=\frac{10}{3}\mathrm{cm} \end{gathered}$$
Magnification = m = $-\frac{v}{u}=\frac{10}{7.5\times 3}$
$$\begin{gathered} \Rightarrow \frac{\mathrm{A}\text{'}\mathrm{B}\text{'}}{\mathrm{AB}}=\frac{10}{7.5\times 3} \\ \Rightarrow \mathrm{A}\text{'}\mathrm{B}\text{'}=\frac{100}{75}=\frac{4}{3}=1.33\mathrm{cm} \end{gathered}$$
Where A'B' is the height of the image.

Hence, the required location of the image is $\frac{10}{3}\mathrm{cm}$ from the pole and image height is 1.33 cm. Nature of the image is virtual and erect.