Question

A person of height h standing at the centre of room looking towards a plane mirror hanging on a wall, can see the bottom edge of the wall behind him if minimum length of the mirror is:

• A. $h$
• B. $h/2$
• C. $h/3$
• D. $h/4$

Answer 1

The correct option is C $h/3$.

From the figure, we have now to calculate just the length of the 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).