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 the 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.