A light device, especially a headlight for motor vehicles, comprises a holding bushing (1), covered by a translucent cover (2), and an inner chamber (3) having mounted there in an optical system (5) for generation of light rays and enabling of controlled selective changes of a light trace on a projection surface. The optical system includes a lens (51) and a light assembly (52) comprising at least one light source and a carrier to carry the light source. The lens is arranged in a fixed position with respect to the position of the translucent cover, and the position of the light assembly is selectively adjustable in a controlled way with respect to the position of the lens by movement of the light assembly in direction (A) and/or by movement in direction (B), wherein the directions (A) and (B) are substantially perpendicular to direction of optical axis (C) of the lens.