a person 1.6m tall is standing at he centres between two walls three metre high.what is the
minimum size of a plane mirror fixed on the wall in front of him, if he is to see full height
of the wall behind him?

The minimum length of the mirror that is required must not be considered from the ground level. The minimum length required is 1m

Dear Student,
Please find below the solution to your problem.

Height of wall h = 3 m
Height of person = 1.6 m
Let us consider height of mirror is h'.
O is the head of the person.
According to figure,
OBC and OB'C' are similar
So,B'C'/BC = O'B'/OB
B'C'/BC = 0.5L / (L+0.5L)
B'C'/BC = 1/3
Now, again
OBA and OB'A' are similar.
O'B'/OB = B'A'/BA
B'A'/BA= 0.5L / (L+0.5L)
B'A'/BA = 1/3
Therefore,
B'C'/BC = B'A'/BA = 1/3
(B'A'+B'C')/(BA+BC) = 1/3
h'/h = 1/3
h' = h/3
h' = 3/3
h' = 1 m
Hence, the minimum size of a plane mirror is 1 m.

Thanks and Regards