Question

A person $1.6\text{m}$ 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?

• A. $0.8\text{m}$
• B. $1\text{m}$
• C. $1.5\text{m}$
• D. $2.3\text{m}$

Answer 1

The correct option is B $1\text{m}$


$\tan \theta =\frac{h_1}{d}=\frac{1.6-h_1}{d/2}$ ... (i)
$\tan \alpha =\frac{h_2}{d}=\frac{1.4-h_2}{d/2}$ ... (ii)
$h_1=\frac{3.2}{3}$ and $h_2=\frac{2.8}{3}$

Hence length of mirror:
$M_1{M}_2=\left(\text{height of wall}\right)-(h_1+h_2)$
$\Rightarrow M_1{M}_2=3-(\frac{3.2}{3}+\frac{2.8}{3})$
$\therefore M_1{M}_2=1\text{m}$
Hence, option $\left(b\right)$ is the correct answer.