Question

Define Principal focus of a plane mirror.

Answer 1

Hint : The principal focus is the point where the rays of light parallel to the principal axis, after reflection converges or diverges. A plane mirror can also be considered as a spherical mirror whose radius of curvature is infinite and the centre of curvature will lie at infinite distance.

Complete step by step answer
Let first understand the meaning of principal focus for a curved mirror. The most common type of curved mirror is a spherical mirror. A spherical mirror has the shape of a section from the surface of a hollow sphere. If the inside surface of the mirror is polished, it is a concave mirror. If the outside is polished, it is a convex mirror.
Principal focus of a mirror is the point at which the rays of light parallel to the principal axis are incident on a spherical mirror all the rays after reflection either converge to a point (in concave mirror) or appear to diverge from a point (in convex mirror) on the principle axis. In other words, focus is an image point on the principal axis for which the object is at infinity.
A plane mirror is considered as the limit of either a concave or a convex spherical curved mirror as the radius & so the focal length becomes infinite.
Mathematically, focal length $\left( f \right)$ of a mirror is the distance between the pole $\left( P \right)$ and focus of the mirror $\left( F \right)$ .
Focal length $\left( f \right)$ is half of the radius of curvature $\left( R \right)$ i.e. $f = \dfrac{R}{2}$ .
Therefore, since the radius of curvature of a plane mirror is infinite, the focal length of a plane mirror will be equal to,
$\Rightarrow f = \dfrac{R}{2} = \dfrac{\infty }{2} = \infty$
Hence, the focus of a plane mirror is at infinity.

Note
Let us understand a few definitions of a spherical mirror.
1. Pole $\left( P \right)$ is the midpoint of a spherical mirror.
2. Centre of curvature $\left( C \right)$ is the centre of the sphere of which the mirror is a part. The distance between the pole of the mirror and the centre of curvature is called the Radius of curvature $\left( R \right)$ .
3. Principal axis: A line passing through $P$ and $C$ i.e. pole and the centre of curvature.
4. Aperture is the effective diameter of the light reflecting area. Intensity of image is directly proportional to the area, which is directly proportional to the square of the aperture.
5. Focal plane: A plane passing from the focus and perpendicular to the principal axis. The formula of the positions of the object and its image is given by:
$\dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f}$ , where $u$ is the object distance, $v$ is the image distance and $f$ is the focal length of the mirror.