# Mathematician proved the impossibility to hide behind the mirrors fully

Mathematician proved the impossibility to hide behind the mirrors fully

To hide the body, you can surround it with a mirrored surface, but all but invisible thus will not be achieved.

Russian mathematician from the Institute of information transmission problems, introduced the “index of visibility” of the body in such a system, and got him to a lower bound, proved different from zero. The paper was published in the journal Proceedings of the Royal Society A.

Scientists are actively working on invisibility, particularly popular over the last decade, it has acquired development using metamaterials. However, there are other approaches. For example, Leonard described an interesting mathematical construct that allows you to make the body invisible in two-dimensional case. He proposed to achieve invisibility by surrounding the body with a lens (a transparent material with variable refractive index).

A conventional mirror is much easier to manufacture and use than hypothetical metamaterials or lenses with varying refractive index, so I wonder is it possible to hide objects from them. It turns out that in three dimensions there are systems that are invisible in three directions, and for two dimensions we can construct the mirror body, which is invisible in n directions, where n is arbitrary.

However, there are restrictions on the possibility of establishing a system of mirrors, completely hiding the body.

In particular, it is proved that there is no perfectly invisible (perfectly invisible) system, that is, one which will not be visible from any point outside it. Moreover, it is assumed that the number of such points has measure zero.

Thus, in reality, full invisibility is usually difficult to achieve. In such cases, we would like to provide at least a partial invisibility (cloak), which makes the object detection is completely impossible, but it greatly complicates. To investigate this problem mathematically, it is necessary to strictly define the visibility index, showing how effectively we hid the body. In their work, the mathematician introduces the index and explores its properties.