Every day we come across mirrors, we can say that their applications are diverse, from small mirrors to large ones that we have in our homes. In them we can see our own image or even the image of any object we place in front of it.
Therefore, we can say that plane mirrors are objects that allow us to see images formed by them.
Regarding these mirrors, we can say that the distance from the object to the mirror is equal to the distance from the image to the mirror, and that the image formed in it has the same size as the object. Therefore, we can say that in a plane mirror, object and image are symmetrical in relation to the plane mirror surface, that is, the distance that separates FOR from the mirror is the same distance between FOR' and the mirror.
Let the frame be fixed at the object point FOR, in front of a flat mirror AND, and FOR' your image. If the mirror translates straightly, in the direction of the straight line passing through FOR and FOR', the mirror will combine the FOR a second image, FOR'', associated with the second mirror position.
In the figure above, the mirror AND move a distance x away from the position 1 to the position 2, and the point image FOR it becomes FOR". Let us study, from the object's point of view, the displacement suffered by the image.
From the figure, it results:
PP'=2d
PP"=2(d+x)=2d+2x
The displacement suffered by the image of point P is:
D=PP"-PP'
D=2d+2x-2d
D=2x
So, we can conclude that if an object is fixed in front of a mirror that translates straightly a distance d, the corresponding translated image, in the same sense as the mirror, a distance 2d.
By Domitiano Marques
Graduated in Physics
Source: Brazil School - https://brasilescola.uol.com.br/fisica/translacao-um-espelho-plano.htm
