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.
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.
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