Question

What must be the minimum length of a plane mirror in which a person can see himself full length? Draw a diagram to justify your answer. Does the distance of a person from the mirror affect the above answer?

Answer 1

Minimum Height Of Plane Mirror Required For A Person To See Full Length Consider a person AB, such that A represents the highest point on his head, and B the lowest point on the foot such that E is the fixed eye level (see figure). The person will be able to see every part of his body if the can see points A and B. Let MN be the minimum length of mirror fixed on the wall, such that the rays AM and BN, after reflection, reach the eye of person, thereby forming an image A₁B₁ when produced backward.

In ∆AEA₁, CM is parallel to AE and C is the mid-point of AA₁. M is the mid-point of A₁E.
Similarly, in ∆BEB₁, ND is parallel to BE and D is the mid-point of BB₁
∴ N in the mid-point of B₁E.
Now in ∆A₁B₁E, M is mid-point of A₁E and N is mid-point of B₁E.
∴ MN is parallel and half of A₁B₁
But, A₁B₁ = AB
So, MN = 1/2 AB.
Thus, in order to see the full length, a person requires a plane mirror which is half his own height. This relation is true for any distance of the object from a plane mirror.