a die for the fresnel lens steps 7 7 as is apparent from the fact that a cross section obtained by cutting the fresnel lens step 7 by a plane including the optical axis has a triangular shape a die for making the lens can be produced by forming by nc machining v shaped grooves corresponding to the respective steps on a die material first as shown in fig2 on a design exit surface k the vector v is determined according to the snell 39 s law from the normal vector n out at the exit point po and the direction vector v out of a refracted ray that passes the point po and is in parallel with the optical axis x x in general the exit surface k is a free surface that cannot be expressed by an analytical function next as shown in fig3 the boundary surface s of refraction and the normal vector n in thereof are determined according to the snell 39 s law from the vector v and the direction vector v in of the incident ray then as shown in fig4 an outer product vector product of the vectors n out and n in is calculated as a vector w which is contained in the boundary surface s and has a direction indicating a forming direction of the boundary surface s fig5 shows a closed curve 10 which is a spline.