Question

The radius of curvature of a plane mirror is
$
  (a){\text{ positive}} \\
  {\text{(b) negative}} \\
  {\text{(c) infinite}} \\
  {\text{(d) none of these}} \\
 $

Answer 1

Hint: In this question keep track of basic characteristics of the image that is formed by a plane mirror generally used in households. That is the image formed is virtual and is laterally inverted. These characterizations of the formed image will help understanding the magnitude of the radius of curvature.

Step by step answer:

Consider the case when we see ourselves in the plane mirror i.e. normal household mirror which we use regularly as our daily basic needs.

So when we see ourselves in a plane mirror the following points we observe:

$\left( i \right)$ Image is virtual
$\left( {ii} \right)$ Image is erect
$\left( {iii} \right)$ Image is of same size i.e. unit magnification.
$\left( {iv} \right)$ Image is laterally inverted (i.e. our right hand appears left hand in the image this is called as laterally inversion).

Phenomenon of lateral inversion through a plane mirror

The light rays which come from the object get reflected from the plane mirror and reach our eyes.

At this point of time our brain feels that the reflected ray is coming from inside the mirror.
This is the reason why the object seems to be laterally inverted.
Now this plane mirror is plane in nature i.e. it is not curved so for the radius of the curvature this plane mirror be the part of the infinite radius sphere so that every part of the sphere resembles a plane mirror.

As the radius of the sphere is infinite, so the radius of the curvature of the plane mirror is infinite.
Now as we know that the focal length of any mirror is twice the radius of curvature so the focal length of the plane mirror is also infinite.
Hence the radius of the curvature of the plane mirror is infinite.
So this is the required answer.

Hence option (C) is the correct answer.

Note: There are certain sign conventions in depicting the sign for radius of curvature. If the vertex is lying to the right of the (COV) center of curvature then the radius of curvature will always be negative, and if the vertex is lying to the left of the center of curvature then the radius of curvature is positive. It is very helpful while dealing with problems of this kind.