Question

A person $1.6\text{m}$ tall is standing at the centre between two walls $3\text{m}$ high. What is the minimum size of a plane mirror fixed on the wall in front of him, if the person wants to see the image of 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 $1\text{m}$

Let O represents the eye of the person standing between the two walls and $M_1{M}_2$ is the height of the mirror.


From the diagram shown in figure,
In $\Delta M_{1}O{O}_1\text{and}\Delta M_1{P}_1{P}_2$
$\tan \theta =\frac{1.4-h_1}{d}=\frac{h_1}{2d}$
$\Rightarrow 2(1.4-h_1)=h_1$
$\Rightarrow h_1=\frac{2.8}{3}\text{m}$
Similarly in $\Delta M_{2}O{O}_1\text{and}\Delta M_2{P}_3{P}_4$
$\tan \varphi =\frac{1.6-h_2}{d}=\frac{h_2}{2d}$
$\Rightarrow 2(1.6-h_2)=h_2$
$\Rightarrow h_2=\frac{3.2}{3}\text{m}$
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.