A floating image interaction device (1; 1'; 1"; 1""), comprising: an imaging optical system (3; 3') including a refracting surface whereby paths of light rays are bent at a plane (3S; 3S'), whereby for an object to be projected placed to one side of said refracting surface, said imaging optical system (3; 3'; 6) forms a real image of said object on the opposite side of said refracting surface with front and back being reversed, wherein said imaging optical system (3; 3') is realized by an imaging optical device comprising of a plurality of unit optical elements (2; 2') realized by dihedral corner reflectors consisting of pairs of mutually perpendicular specular surfaces (21, 22; 21', 22') reflecting light and arranged perpendicularly or nearly perpendicularly to an optical device plane (3S; 3S') corresponding to said refracting surface, thereby functioning as a dihedral corner reflector array, whereby for the object to be projected placed to one side of said optical device plane (3S; 3S'), its real image will be formed on the opposite side of said optical device plane (3S; 3S') by said plurality of unit optical elements (2; 2'), characterized by a user object detecting means capable of measuring the position, or the position and shape of a user object approaching said real image and detecting the position, or position and shape of said user object by using information based on that measurement; and a real image modifying means capable of using the position, or position and shape of said user object as detected by said user object detecting means to modify said real image in order to follow the position, or position and shape of said user object in relation with said real image. an imaging optical system (3; 3') including a refracting surface whereby paths of light rays are bent at a plane (3S; 3S'), whereby for an object to be projected placed to one side of said refracting surface, said imaging optical system (3; 3'; 6) forms a real image of said object on the opposite side of said refracting surface with front and back being reversed, wherein said imaging optical system (3; 3') is realized by an imaging optical device comprising of a plurality of unit optical elements (2; 2') realized by dihedral corner reflectors consisting of pairs of mutually perpendicular specular surfaces (21, 22; 21', 22') reflecting light and arranged perpendicularly or nearly perpendicularly to an optical device plane (3S; 3S') corresponding to said refracting surface, thereby functioning as a dihedral corner reflector array, whereby for the object to be projected placed to one side of said optical device plane (3S; 3S'), its real image will be formed on the opposite side of said optical device plane (3S; 3S') by said plurality of unit optical elements (2; 2'), characterized by a user object detecting means capable of measuring the position, or the position and shape of a user object approaching said real image and detecting the position, or position and shape of said user object by using information based on that measurement; and a real image modifying means capable of using the position, or position and shape of said user object as detected by said user object detecting means to modify said real image in order to follow the position, or position and shape of said user object in relation with said real image.