Question

A small girl of height 1 m can just see her image in a vertical plane mirror 4m away from her. Her eyes are 0.92 m from the floor. In order that she sees her full image in the mirror, the shortest vertical dimension of the mirror is
A. 0.5 m
B. 0.7 m
C. 0.46 m
D. 0.56 m

Answer 1

Hint: The portion of the image that the person can see depends on the vertical size of the mirror. If the size of the mirror is not sufficient, then the person will not be able to his or her full image. It only depends on the height of the person.

Formula used:
${{H}_{m}}=\dfrac{H}{2}$
Here, H is the height of the person and ${{H}_{m}}$ is the minimum height of the mirror.

Complete step by step answer:
It is given that a girl is standing in front of a plane mirror. We have to find the minimum vertical height of the plane mirror for which she can see her full image. When a person stands in front of a plane mirror, the person can see an erect image of his or her inside the mirror. The distance of the image from the mirror is equal to the distance of the person from the mirror and even the size of the image is exactly equal to the object.

However, the portion of the image that the person can see depends on the vertical size of the mirror. If the size of the mirror is not sufficient, then the person will not be able to his or her full image. The minimum vertical height for which the person can see his or her image is found to be equal to ${{H}_{m}}=\dfrac{H}{2}$.
Here, H is the height of the person and ${{H}_{m}}$ is the minimum height of the mirror.
It is given that the height of the girl is 1 m. This means that $H=1m$.
Therefore,
${{H}_{m}}=\dfrac{1}{2}\\
\therefore{{H}_{m}}=0.5m$.
This means that the minimum vertical height of the mirror for which the girl can see her full image is equal to 0.5m.

Hence, the correct option is A.

Note: There is one more condition to see the full image and it is that the mirror must be placed at a height of $\dfrac{{{H}_{E}}}{2}$, where ${{H}_{E}}$ is the height of the eyes above the ground. Note that the minimum height of the mirror to see the full image does not depend on the distance between mirror and the person.