Question

A man is standing exactly at midway between a wall and a mirror and he want to sce the full height ofthe wall (behind him) in a plane mirror (in front of him). If the height of wall is $H$ , then the minimumm length of mirror should be

• A. $\frac{H}{4}$
• B. $\frac{2H}{3}$
• C. $\frac{H}{3}$
• D. $\frac{H}{5}$

Answer 1

The correct option is C $\frac{H}{3}$

From the figure we can see that $\Delta EFG$ and $\Delta CDG$ are similar.

$\therefore \frac{FE}{CD}=\frac{GI}{GK}$

$\Rightarrow \frac{FE}{H}=\frac{d/2}{d/2+d}=\frac{1/2}{3/2}=\frac{1}{3}$

$\Rightarrow FE=\frac{H}{3}$

Hence the correct answer is option (C).