Question

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

Answer 1

The mirror formula is:
$\frac{1}{f} = \frac{1}{u} + \frac{1}{v},$
where $f = +15 \, \text{cm}$ (convex mirror), $u = -10 \, \text{cm}$ (object distance), and $v$ is the image distance.
Substitute the values:
$\frac{1}{15} = \frac{1}{v} + \frac{1}{-10}.$
Simplifying:
$\frac{1}{v} = \frac{1}{15} + \frac{1}{10} = \frac{2 + 3}{30} = \frac{5}{30}.$
$v = \frac{30}{5} = +6 \, \text{cm}.$
Thus, the image is formed 6 cm behind the mirror.