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.
Solution and Explanation
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.
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Notes on Spherical Mirrors
Concepts Used:
Spherical Mirrors
A spherical mirror is a mirror which has been cut out of a spherical surface.
There are two kinds of spherical mirrors:
- Convex Mirror
- Concave Mirror
Concave Mirror
Concave mirrors are also called converging mirrors, because in these types of mirrors, light rays converge at a point after impact and reflect back from the reflective surface of the mirror.
Convex Mirror
The convex mirror has a reflective surface that is curved outward. Regardless of the distance between the subject and the mirrors, these mirrors are "always" virtual, upright and reduced.