Focal length of a plane mirror is infinity. (A plane mirror can be considered as a spherical mirror of infinite radius of curvature. Focal length is half of radius of curvature and hence it is infinity.

The focal length of a plane mirror is infinity.

Explanation:

Definition of Focal Length:
The focal length of a mirror is the distance between the mirror and the focal point. It is denoted by the symbol 'f'.

Plane Mirror:
A plane mirror is a flat and smooth reflecting surface. It reflects light rays in such a way that the image formed is virtual, erect, and of the same size as the object. The image is formed behind the mirror and at an equal distance as the object is in front of the mirror.

Focal Length of a Plane Mirror:
Since a plane mirror is a flat surface, it does not have a curvature like concave or convex mirrors. The focal length of a mirror is defined as the distance between the mirror and the focal point. In the case of a plane mirror, there is no curvature and hence no focal point. Therefore, the focal length of a plane mirror is considered to be infinity (∞).

Reasoning:
The focal length of a mirror is determined by the curvature of the mirror surface. In the case of a plane mirror, there is no curvature, and thus, no focal point. The light rays that are incident on a plane mirror are reflected at the same angle as the incident angle, resulting in a virtual image. Since the image formed is virtual and appears to be formed behind the mirror, the focal length is considered to be infinity.

Significance:
Knowing the focal length of a mirror is important in understanding the characteristics and properties of the mirror. For a plane mirror, having a focal length of infinity means that the image formed is always virtual, erect, and of the same size as the object. It also helps in determining the position and properties of the image formed by the mirror.

In conclusion, the focal length of a plane mirror is considered to be infinity because there is no curvature and no focal point.