Question #303a3

1 Answer
A08
Apr 3, 2017

A)

Explanation:

Quora, edited
In the figure above let AB is a person. A"B" is his image as seen by him in the mirror.

Let a ray of light start from B, hit the mirror at B', get reflected and enter eye at E. The image of B is formed at B". Similarly image of eye E is formed at E", where E E' hits the mirror making an angle of incidence of 0^@. We see that for part height EB the required length of mirror is E'B'

Now if we draw a normal B'N as shown,
length EN=E'B' .......(1)

In Delta EB'N and Delta NBB'

  1. From laws of reflection we know that angle of incidence is equal to angle of reflection.
  2. Angles at N=90^@
  3. Side B'N is common.

=> Triangles are congruent (ASA).
=> sides EN=NB ......(2)

Combining (1) and (2) we get
E'B'=1/2EB .....(3)
Similarly it can be shown that
A'E'=1/2AE ......(4)

Combining (3) and (4)
Total height of the mirror required A'B'=1/2AB.

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