# mirror translation

We know that plane mirrors are objects that allow us to see images formed by them. We can see that they are used in different places, such as in cars, bathrooms, etc.

Regarding these mirrors, we can say that the distance of the object from the mirror is equal to the distance of the image from the mirror, and that the image formed in it has the same size as the object.

The case that we will analyze next deals with the displacement of a plane mirror in relation to an object at a fixed point. Let us consider any point F , which is situated at a distance d from a plane mirror (figure below), where F’ is the image formed of F .

Considering fixed the pointF , let the mirror move parallel to itself, undergoing a displacement x , as shown in the figure below. According to these conditions, the new image that will be formed of F is F’ ‘, where y is the displacement suffered by the image.

According to the figure below, we have the following equation:

2d + y = d + x + d + x
2d + y = 2d + 2x
2d – 2d + y = 2x
y = 2x
Thus, we can conclude that the displacement of the image is twice the displacement of the mirror.

If we consider that the displacements occurred in the same time interval, we can conclude that the image speed ( Vi ) is twice the mirror speed ( Ve ).

Vi = 2 Ve

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