Suppose you are standing 1 m in front of a plane mirror. What should be the minimum vertical size of the mirror so that you can see your full image in it ?

To see a full image in a plane mirror, the minimum vertical size of the mirror must be half of the person's height. This is a fundamental principle of geometrical optics derived from the laws of reflection. When a person looks at their own image, the light rays from the top of the head and the feet must reflect off the mirror and reach the eyes. Due to the law of reflection (angle of incidence equals angle of reflection), the point on the mirror where the ray from the feet reflects is exactly halfway between the eyes and the feet. Similarly, the ray from the top of the head reflects at a point halfway between the eyes and the top of the head. Consequently, the total vertical length of the mirror required is exactly half the height of the person. This requirement is independent of the distance between the person and the mirror.