Answer :

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 A_{1}B_{1}, when produced backward.

In ΔAEA_{1}, CM is parallel to AE and C is the mid-point of AA_{1}.

M is the mid-point of A_{1}E.

Similarly, in Δ BEB_{1} ND is parallel to BE and D is the mid-point of BB_{1},

N is the mid-point of B_{1}E.

Now in Δ A_{1}B_{1}E, M is the mid-point of A_{1}E and N is the mid-point of B_{1}E.

MN is parallel to and half of A_{1}B_{1}.

But A_{1}B_{1} = 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.

Rate this question :

If we want to seeRajasthan Board Science

What is lateral iRajasthan Board Science

What is regular rRajasthan Board Science

An incident ray oRajasthan Board Science

What type of our Rajasthan Board Science

When any object aRajasthan Board Science