Abstract: A lens for a lamp having a non-planar portion in which a large number of Fresnel lens steps or prism steps are formed on the incident surface thereof, yet which produces a very parallel output beam. The lens steps are defined by a tangential vector at an arbitrary point of a refraction boundary surface (Fresnel lens steps) or a total-reflection surface (prism steps) which is in the same direction as an outer product of a normal vector of the refraction boundary surface or total-reflection surface and a normal vector of an exit surface of the lens at a refraction point where a ray refracted by the refraction boundary surface or total-reflection surface is refracted. A method is also disclosed for producing a die for forming such a lens.