Question

There is a point object and a plane mirror. If the mirror is moved 10 cm away from the object, find the distance which the image will move.

Answer 1

Hint: Objects kept in the front of a mirror form an image at a distance behind the mirror such that separation of the mirror and the object is the same as the separation of the image and the object.

Complete answer:
We assume that initially there is no separation between the object and the mirror. So, the object and the mirror coincide. Consider the figure (grey circles are point objects).

Now, if we move the object 10 cm apart from the mirror, we can see that the image will also move 10 cm behind the mirror.

Initially, we observed no separation between the object and its image or we can say that the object and image were separated by 0 cm as our object is a point object. But as the object is taken away from the mirror, the image moves away by the same distance. Therefore, the distance of the image from the mirror now is 10 cm.
But, the distance of the image from the object is 10 cm of object from mirror plus 10 cm of image behind the mirror i.e.,
10 cm + 10 cm = 20 cm
Therefore, when our point object moved away from the mirror by 10 cm, the image of it moved away from it by twice the distance it moved, i.e. 20 cm.

Additional Information:
Unlike plane mirrors, the object distance is different from the image distance in spherical mirrors. A daily life example is the rear view mirror in vehicles. It uses a convex mirror and has written on it: "objects in the mirror are closer than they appear." Thus, we require spherical mirror formulas in such cases.

Note:
The question itself provides us an ideal circumstance that the object is a point object. Had there not been a point object, our assumption that initial separation was 0 cm might not have worked in such condition.