1. A floating image interaction device, comprising: distortion-free imaging optical system including a surface at which paths of light rays are bent by means of mirror surface reflection; and a user object detecting means, wherein for an object to be projected placed to one side of said surface, said imaging optical system forms a real image of said object on the opposite side of said surface with front and back being reversed, the imaging optical system is for forming a two-dimension real image of a two-dimension object to be projected, and a three-dimensional real image of a three-dimension object to be projected; the real image can be observed from oblique direction of the surface; and said user object detecting means capable of detecting the position, or the position and shape of user objects approaching said real image.