Question

What should be the minimum height of the mirror so that a person can see the full wall of height h behind him? (Assume the man to be at the centre of the wall and the mirror.)

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

Answer 1

The correct option is B $\frac{h}{3}$

We need the minimum height of the mirror, which means we are talking about the extreme case here. The condition is simple : " Rays from the extreme ends of the wall after hitting the mirror must reach the eye". Let us draw the ray diagram, given this and solve the geometry.

Now, the angles $\angle 1$ and $\angle 2$ are equal, applying the law of reflection. Also, $\angle 3$=$\angle 2$, as they are alternate interior angles.
Therefore, the shaded triangles are similar.
By using the law of similarity.
$\frac{d}{s}=\frac{x/2}{8/2}Weget,x=d.Also,3d=h,Hence,x=\frac{h}{3}$