Previous Year Question
To look at the total image of a person, the minimum height of a plane mirror is:
Equal to the height of a person
Half of the height of a person
One fourth of the height of a person
Two times the height of a person
Correct Answer: B
Detailed Solution
Let the total height of a person be H. To see the complete body, two extreme rays must reach the eyes after reflection—one from the top of the head and the other from the feet.
According to the Law of Reflection—
For the ray coming from the head to the eye, the upper edge of the mirror needs to extend only up to the midpoint between the eye and the top of the head.
Similarly, for the ray coming from the feet to the eye, the lower edge of the mirror needs to extend only up to the midpoint between the eye and the feet.
If the distance from the eye to the top of the head is , and the distance from the eye to the feet is , then—
The required mirror height is—
Thus, the minimum height of a plane mirror required to see the complete image of a person is half the person's total height.
An important fact is that this minimum height is independent of the distance between the person and the mirror. Moving closer to or farther from the mirror does not change the theoretical minimum mirror height of H/2.