Prove that the length of the mirror required to view the complete image of an object is half of
the height of the object.
Answers
Example The man is twice as tall as the distance between points X and Y. In other words, to view an image of yourself in a plane mirror, you will need an amount of mirror equal to one-half of your height. A 6-foot tall man needs 3-feet of mirror (positioned properly) in order to view his entire image.
Answer:
Solution -
One can see his full image in a mirror half their height irrespective of their distance from the mirror.
The only thing is that the elevation of top of this mirror should be exactly halfway between the level of eyes and the top of one's head.
AB is a person. A"B" is his image as seen by him.
From laws of reflection, it turns out that length B'E' is half of length BE. Similarly A'E' is half of AE. Total height of the mirror required is A'B'. Which is half of the total height AB.
Proof :
MN is plane mirror
HF is boy standing in front of the mirror
H denotes head of the boy, E denotes eyes of the boy and F denotes feet of the boy.
A ray HM emerges from the head of the boy and is incident at the uppermost end M of the mirror from where it is reflected as ray ME and enters the eyes E of the boy.
Now, the rayFN emerges from feet F of the boy. It is incident at N ,the lowest end of mirror from where it is reflected and reflected ray NE enters the eyes of the boy.
From the geometry of the figure,
MN= KL= KE+EL=(1/2)HE+(1/2)EF=(1/2)(HE+EF)=(1/2)HF.
But, MN is height of mirror which is seen to be half the height HF of the boy.