Question

How many types of spherical mirrors are there? Write their names. Give the definition of centre of curvature and principal axis of a spherical mirror. Focal length of a convex mirror is 30 cm. An object of length 5 cm is placed in front of a mirror at a distance of 30 cm. Find the position, size, and nature of the image.

Hint:

In convex mirrors, the image formed is always virtual, erect, and smaller than the object, regardless of the object distance.

Answer 1

There are two types of spherical mirrors:
1. Concave mirror: A mirror with an inward-curved reflecting surface.
2. Convex mirror: A mirror with an outward-curved reflecting surface.

Centre of Curvature and Principal Axis:
- Centre of Curvature (C): The centre of the sphere of which the mirror is a part. It lies on the principal axis.
- Principal Axis: The line passing through the centre of curvature and the pole of the mirror. It is the axis of symmetry of the mirror.
For the given convex mirror:
- Focal length (f): 30 cm (given)
- The object distance (\(u\)) = -30 cm (object is in front of the mirror)
- The object height = 5 cm (given)
Using the mirror formula:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Substituting the values:
\[ \frac{1}{30} = \frac{1}{v} + \frac{1}{-30} \] Solving for \(v\):
\[ \frac{1}{v} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} = \frac{1}{15} \] Therefore, \(v = 15 \, \text{cm}\).
The image is formed at a distance of 15 cm behind the mirror, indicating that it is a virtual image. Since the image is formed behind the mirror, the image will be diminished and erect.

Conclusion:
The image formed by the convex mirror is virtual, diminished, and erect, with a position 15 cm behind the mirror.