Question

An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

Answer 1

Focal length of convex mirror, $f = +15\ cm$
Object distance, $u = −10\ cm$
According to the mirror formula,
$\frac 1v-\frac 1u=\frac 1f$

$\frac 1v=\frac 1f-\frac 1u$

$\frac 1v=\frac {1}{15}+\frac {1}{10}$

$\frac 1v=\frac {25}{150}$

$\frac 1v = \frac 16$
$v=6\ cm$
The positive value of v indicates that the image is formed behind the mirror.
Magnification, $m=-\frac {\text {Image\ distance}}{\text {Object\ distance}}$
$m =-\frac vu$

$m=-\frac {6}{-10}$

$m =+0.6$

The positive value of magnification indicates that the image formed is virtual and erect.