If we want to see our full image in the plane mirror then what should be a minimum height of mirror?

If the height of a person is height , then to view the full image of himself from head to toe the mirror should be at least of height.

Derivation

Consider a person AB, such that A represents the highest point on the head, B, the lowest point on foot and E is the fixed eye level. The person will be able to see every part of his body if he can see points A and B. Let MN be the minimum length of mirror fixed on the wall, such that rays AM and BN, after reflection, reach the eye of a person, thereby forming image A₁B₁, when produced backward.

In ΔAEA₁, CM is parallel to AE and C is the mid-point of AA₁.
M is the mid-point of A₁E.
Similarly, in Δ BEB₁ ND is parallel to BE and D is the mid-point of BB₁,
N is the mid-point of B₁E.
Now in Δ A₁B₁E, M is the mid-point of A₁E and N is the mid-point of B₁E.
MN is parallel to and half of A₁B₁.
But A₁B₁ = AB
MN = AB
Thus in order to see the full length of a person, requires a plane mirror, which is half of its own height. This relation is true for any distance of the object from a plane mirror.