Here we derive the condition for the minimum size of a mirror to see full image of a man standing in front of the mirror.
Let us consider a plane mirror XY is placed in front of an object larger than it. Let AB be the man standing in front of the mirror where A is his head and B is his foot. Here C is his eyes. When a ray, AD strikes to the mirror, it gets reflected to his eyes C and he sees his head. Similarly a light ray from BF strikes the mirror, it gets reflected to his eyes and he sees his foot.
Using the basic geometrical laws, we can say from figure:
AP = PC = DE
To see a foot of the mirror,
CG = GB = EF
Now, minimum size of the mirror = DE + EF
= PC + CG (Since DE = PC and EF = CG)
= 1/2 AC + 1/2 CB
= 1/2 (AC + CB)
= 1/2 AB
From the given figure, we can conclude that the minimum size of the mirror to see the full size of a person is half of that object.