Question

A man stands $ 20m $ in front of a large plane mirror. How far must he walk before he is $ 10m $ away from his image?

Answer 1

Hint: Plane mirrors form images that are upright just like us. These upright images are called erect images. They never form inverted images. Also, the size of the image is exactly the same as our original size. But there is one difference between the image formed in the plane mirrors and the object is the left-right reversal. If we raise the left hand then the object in the mirror will be on the right side. These images are called laterally inverted images.

Complete Step By Step Answer:
Now let us see how the images in the plane mirror behave as we move. If we move forward to the plane mirror then the image also moves towards the mirror and vice versa. If we stand $ 10m $ behind the mirror then the object in the mirror also will stand $ 10m $ behind the mirror. This can be said like the image distance is the same as the object distance in a plane mirror. This principle is what we are going to use in the above-given problem.
Given that a man is standing $ 20m $ in front of the large plane mirror. Therefore the object in the mirror is also $ 20m $ . Therefore the distance between the object and image is $ 20 + 20 = 40m $ .
It is asked how far the man should be walking to be $ 10m $ from his image.
This means that the distance between the object and the mirror $ = \dfrac{10}{2} =5m $
This is because we know that the plane mirror forms an image of the object at the same distance behind it as it is between the object and the mirror. Therefore, $ 5 + 5 = 10m $
Therefore the distance the man should walk before he is $ 10 $ m away from his image is $ 20m - 5m = 15m $ towards the mirror.
Correct Answer:
Therefore he should walk $ 15m $ so that he is $ 10m $ away from his image.

Note:
We have seen that the image formed by the plane mirror is a lateral image. Lateral literally means sideways. Lateral inversion is the apparent reversal of the mirror image’s left and right when compared with the original object that is in front of the plane mirror. We can see this in Ambulances as every letter in the ambulance vehicle will be the mirror image of the ambulance so that people in the vehicle in front of the ambulance vehicle will see the proper image and pave a way to the ambulances.