Question

A person wants to see AB part of his image (see Fig.). His eye level is at 1.8m above ground. He uses the minimum size of mirror required for this, finding the height of the lowest point of mirror above the ground.

Answer 1

Hint: The size of the mirror will be minimum when the length is half of its total length. The height from ground to B and ground to A are given in the question. Hence calculate the total length and then dividing the total length by two we obtain the half length which is the minimum size of the mirror. The height above required is half of the height from his eyes to A. This is the height from the level of A. Thus we have to calculate the height from the ground.


Complete step-by-step solution:
At half of his total length the size of the mirror will be minimum.
That is,
\[\dfrac{1.5-1}{2}=\dfrac{0.5}{2}\]
Then the height above required = (height from his eyes to A) /2
$\begin{align}
  & =\dfrac{1.8-1}{2} \\
 & =\dfrac{0.8}{2} \\
 & =0.4 \\
\end{align}$
This is the height from the level of A.
Thus we have to calculate the height from the ground.
 From ground,
$H=0.4+1=1.4m$
Therefore the height of the lowest point of the mirror above the ground is 1.4m.

Note: In order to see the full image of a person’s height the mirror should be at least half of the person’s height. This is because that in the case of reflection of an object, the angle of incidence and reflection must be equal. That if a man is 150cm tall then a 75cm mirror is required to see his full height in a mirror