Question

A man stands in a room with his eyes at the center of the room. The height of the ceiling is $H$. The length of the shortest plane mirror, fixed on the wall in front of the man, so that the man can see the full image of the wall behind him is:

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

Answer 1

Answer: (C)

$\frac{H}{3}$

From the figure , we have now to calculate just the length of mirror that is $2x$

Now, in $\Delta OAB$ and $\Delta DAC$

We see that these are similar triangles.

Hence, $\frac{AB}{OB}=\frac{AC}{CD}$

$⟹\frac{x}{L/2}=\frac{\frac{H}{2}-x}{L}$

$⟹2x=\frac{H}{2}-x$

$⟹3x=\frac{H}{2}$

$⟹2x=\frac{H}{3}$= required length of mirror.

Hence, answer is option-(C).