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.