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.