Question

According to question A man is standing in just b/w the mirror and a wall of height 'h' . separation of mirror and wall is 'd' .Find length of mirror required so that man can completely see the wall in mirror at standing on the same distance where he was i.e. d/2

Answer 1

Let HB be the wall with height h and MM' is the mirror. Man standing at distance x from mirror and the wall is at distance y from man.

Let MM' be r, then,

EA=EG=HF=DB=MM'=r --------(1)

in Triangle RMB, C is midpoint of BA and CA is parallel to RM

A is midpoint of BM.

I is the midpoint of QH, G is midpoint of HM'

in triangle MFB, A is midpoint of BM and AE is parallel to BF.

E is midpoint of MF.

from midpoint theorem,

In triangle M"DH, E is midpoint of M'D

Therefore,

2EA=FB=

and 2GE=HD which meanss HD=FB =2r  --------(2 eq)

from eq 1 and 2 we get,

HD=HF+HD=r+FD=2r

FD=r

therefore, HD=FD=BD=r

HB=HD+FD+Bd=3r

h=3r

r=h/3

Therefore, to see the complete wall infront of height H in the mirror the person will require plane mirror of 1/3 of height of wall.