How will you distinguish between a plane mirror, concave mirror and a convex mirror, without touching them?

Hint: You can start by describing the types of images formed when the object is kept at different distances from a plane mirror, concave mirror and a convex mirror. Then explain how we can actually place an object at various distances from the mirror and note the type of images formed to figure out the solution.

Complete step by step answer:
To attempt the solution we have to first understand what kind of image is formed in the case of a plane mirror, concave mirror and a convex mirror.
Plane mirror - The image formed by a plane mirror is always upright, virtual and the same size as the object no matter where the object is placed in front of the mirror.
Concave mirror – The image formed by a concave mirror is inverted, real and diminished if the object is at a distance more than the focus. The image formed is inverted, real and the same size as the object if the object is kept at the focus. The image formed is upright, virtual and enlarged if the object is kept at a distance less than the focus.
Convex mirror – The image formed by a convex mirror is always upright, virtual and diminished no matter the distance of the object from the mirror.
To distinguish between a plane mirror, concave mirror and a convex mirror, we take an object and keep it at varying distance from the mirror and notice the nature of the image formed.
If the image formed is always upright, virtual and the same size as the object then it is a plane mirror.
If the image formed is sometimes inverted, real and diminished, sometimes inverted, real and the same size as the object and sometimes is upright, virtual and enlarged. Then it is a concave lens.
If the image formed is always upright, virtual and diminished, then it is a convex mirror.

Note: The method used to solve this problem is very similar to the working of an optical bench. An optical bench is an optical instrument used to find the focal length, nature, etc. of mirrors and lenses. Here also we keep the object at varying positions and observe the images formed to find the required data.