Question

A person 1.6m tall is standing at the center between two wall 3m high. What is the minimum size of a plane mirror fixed on the wall in fort of him ,if he is see the full height of the wall behind him?

Answer 1

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Answer 2

Answer: $h' = 1 m$

Explanation:

Given that,

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,

$\Delta$OBC and $\Delta$OB'C' are similar.

So, $\dfrac{B'C'}{BC} = \dfrac{OB'}{OB}$

$\dfrac{B'C'}{BC} = \dfrac{\dfrac{L}{2}}{L+\dfrac{L}{2}}$

$\dfrac{B'C'}{BC} = \dfrac{1}{3}$

Now, again

$\Delta$OBA and $\Delta$OB'A' are similar.

$\dfrac{O'B'}{OB} = \dfrac{B'A'}{BA}$

$\dfrac{B'A'}{BA} = \dfrac{\dfrac{L}{2}}{L+\dfrac{L}{2}}$

$\dfrac{B'A'}{BA} =\dfrac{1}{3}$

Therefore,

$\dfrac{B'C'}{BC} = \dfrac{B'A'}{BA} = \dfrac{1}{3}$

$\dfrac{B'A'+B'C'}{BA+BC} = \dfrac{1}{3}$

$\dfrac{h'}{h} = \dfrac{1}{3}$

$h' = \dfrac{h}{3}$

$h' = \dfrac{3}{3}$

$h' = 1 m$

Hence, the minimum size of a plane mirror is 1 m.