Question

A man is standing at distance x from a a plane mirror in front of him. He wants to see the entire wall of height h in mirror which is at a distance y behind he man. Find the minimum size of the mirror required

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.

Answer 2

h/3

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