# Minimum Size of a Mirror to See Full Image of a Man

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

Again,

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.

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