Question

A man is standing at distance x from 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 the man. Prove that the minimum size of mirror required is hx/(y+2x)

Answer 1

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 M FB, A is midpoint of BM and AE is parallel to BF E is midpoint of MF from the midpoint theorem in triangle M"DH,E is midpoint of M'D
2EA=FB=and 2GE=HD which meanss HD=FB=2r.....(2)
from equation 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 in front of height H in the mirror the person will require plane mirror of 1/3 of height of wall