Question

A man stands $10{\text{m}}$ in front of a large plane mirror. How far must he walk before he is $5{\text{m}}$ away from his image?

Answer 1

Hint: We are given the distance between the plane mirror and the object which is the man standing in front of the mirror. We need to be clear with the concepts of image formation by a plane mirror and need to find the distance between the image and object.

Complete answer:
We are given the initial distance between the object and the mirror. We need to find the final distance between the object and the mirror when the image is $5{\text{m}}$ away from the object.In this case, we have the man standing at a distance of $10{\text{m}}$ which means that the image of the man will be $10{\text{m}}$ away from the mirror too because in a plane mirror the distance between the image and the object is the same and the image formed is always a virtual image.

Therefore initially the distance between the man and his image is $20{\text{m}}$ . If the image is $5{\text{m}}$ away from the man that means the man is $2.5{\text{m}}$ away from the mirror. Thus the distance he must cover is $10{\text{m - 2}}{\text{.5m = 7}}{\text{.5m}}$ towards the mirror.

Note: A plane mirror always forms a virtual image (behind the mirror). The image and object are the same distance from the plane mirror, the image size is the same as the object size, and the image is upright. The difference between a virtual image and a real image is that a virtual image cannot be projected on a screen. You cannot distinguish a real image from a virtual image simply by judging from the image perceived with your eye.