  This work is related to billiards and their applications in geometric optics.
It is known that perfectly invisible bodies with mirror surface do not exist.
It is natural to search for bodies that are, in a sense, close to invisible. We
introduce a {\it visibility index} of a body measuring the mean angle of
deviation of incident light rays, and derive a lower estimate to this index.
This estimate is a function of the body's volume and of the minimal radius of a
ball containing the body. This result is far from being final and opens a
possibility for further research.
