Question

The man, whose height is 1.75 m is standing at a distance 6 m from a vertical pillar of height $$h=7\text{m}$$. At what distance from the man should we put a small flat mirror on the ground horizontally to see in the image of the pillar?
A. 4.8 m
B. 1.2 m
C. 5.2 m
D. 4.2 m

Answer 1

Hint: In order to see the top of the pillar in the mirror, the light ray reflected from the top of the pillar should reflect from the surface of the mirror and reach the eyes of the man. Use the law of reflection to determine the properties of the triangles made by the incident ray and reflected ray. Use congruent ratio rule to determine the distance of the flat mirror from the man.

Complete step by step answer:
We have given that the mirror is placed horizontally on the ground and the man can see the top of the pillar in the flat mirror. Let the distance between the man and the flat mirror is x meter. Therefore, the distance between the flat mirror and the pillar is $$\left(6-x\right)\text{m}$$.In order to see the top of the pillar in the mirror, the light ray reflected from the top of the pillar should reflect from the surface of the mirror and reach the eyes of the man as shown in the following figure.

Let us recall the law of reflection. We know that when the light ray reflects from the flat mirror, the angle of incidence is equal to the angle of reflection. Also, from the above figure, since the angle of incidence and the angle of reflection is the same, the angle $$\theta$$ shown in the above figure should also be the same. Thus, we can write, from the congruent ratio rule,
$${\displaystyle \frac{1.75}{x}}={\displaystyle \frac{7}{6-x}}$$
$$\Rightarrow 1.75\left(6-x\right)=7x$$
$$\Rightarrow 10.5-1.75x=7x$$
 $$\therefore x=1.2\text{m}$$
Thus, the distance between the man and the flat mirror should be 1.2 m.

So, the correct answer is option B.

Note:The angle $$\theta$$ shown in the above figure is not the angle of incidence or the angle of reflection. The incidence angle should be measured between the incident ray and the normal and the same for the angle of reflection. To answer this question, the crucial step is to use laws of reflection and therefore, students must memorize all the laws of reflection.