Question

A person of height $200\text{cm}$ is standing in front of a plane mirror. Find the minimum height of the mirror required, so that the person can see his full size image.

• A. $50\text{cm}$
• B. $200\text{cm}$
• C. $100\text{cm}$
• D. It depends on the distance of person from the mirror.

Answer 1

The correct option is C $100\text{cm}$


Let $HF$ be the height of the person and $E$ be the eye level. Draw the rays $H{M}_1$ and $F{M}_2$ incident at the edges of the mirror. Complete ray diagram is as shown in the figure.

From the figure, height of mirror $M_1{M}_2=x+y$
& height of person $HF=2x+2y=2(x+y)$

$\therefore \frac{M_1{M}_2}{HF}=\frac{x+y}{2(x+y)}=\frac{1}{2}$

$\Rightarrow \frac{M_1{M}_2}{200}=\frac{1}{2}\Rightarrow M_1{M}_2=100\text{cm}$

Note:- The required height of the mirror is half the height of the person.