Question

A person 1.6 m tall is standing at the centre 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 the full height of the wall behind him

Answer 1

The full height of the wall behind him is 1 m.

Step-by-step explanation:

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,

ΔOBC and ΔOB'C' are similar.

So, B'C'/ BC = OB' / OB

B'C'/ BC = L/2 ÷ L + L/2

B'C'/ BC = 1/3

Now, again

ΔOBA and ΔOB'A' are similar.

O'B' / OB = B'A' / BA

B'A' / BA =  L/2 ÷ L + L/2

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 full height of the wall behind him is 1 m.

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