Question

An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of a focal length of 18 cm. At what distance from the mirror should a screen be placed so that a sharply focused image can be obtained? Find the size and the nature of the image.

Answer 1

Step (1) Given:

The object distance, $u=–27cm$ (object distance should be taken negatively)

Focal length,$f=–18cm$ (Focal length of a concave mirror is taken negatively)

Object size, $h_0=7.0cm$

Step (2) Finding the image distance using the mirror formula:

We know the mirror formula that

$$\begin{gathered} \frac{1}{v}=\frac{1}{f}-\frac{1}{u} \\ \frac{1}{v}=\frac{-1}{18}+\frac{1}{27}=\frac{-1}{54} \\ v=-54cm \end{gathered}$$

The screen must be placed at a distance of 54 cm from the mirror in front of it.

Step (3) Finding the size of the image:

$$\begin{gathered} \frac{h_i}{h_0}=-\frac{v}{u} \\ \frac{h_i}{7}=-(-54/-27) \\ {h}_i=-2x7=-14cm \end{gathered}$$

Thus, the image is of 14 cm length and is real, inverted and magnified image.