Question

An object 2cm high is placed at a distance of 16cm from a concave mirror which produces a real image 3cm high.
(i) Find the position of the image.
(ii) What is the focal length of mirror?

Answer 1

Here h₁​ = 2 cm, u = -16 cm, h_2​ = -3 cm (Since image is real and inverted.)

(i) Position of image

\(\because m = \frac{h_2}{h_1} = - \frac vu\)

\(\therefore v = \frac{-h_2}{h_1}u\)

\(= \frac 32 \times (-16)\)

\(= - 24\) cm

(ii) Focal length of mirror

\(\frac 1f = \frac 1v + \frac 1u\)

\(= -\frac 1{24} - \frac 1{16}\)

\(= \frac{-2 - 3}{48}\)

\(= \frac {-5}{48}\)

\(f = \frac{-48}5\)

\(= -9.6\) cm

Answer 2

The image is formed at distance of 24cm in front of the mirror (negative sign means object and image are on the same side).