A novel beam demagnifier(a cone) is presented based on total internal reflection-refraction principle, and the light propagation characteristics inside the cone were studied by using ray-tracing method and computer simulation. This paper presents several proof-theoretic results concerning a cone as a beam demagnifier under certain conditions. When the semiapex angle of the cone is equal to a series of specific values an output beam is parallel to an incident beam, the beam's diameter narrows, and the demagnification ratio of the cone is a function of apex angle and there exists a series of extreme points; the demagnifier can be used in series so as to further narrow or magnify the diameter of incident beam.
