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The aim of the present work is to introduce a lens whose faces are a conicalsurface and a spherical surface. We illuminate this lens by a plane wavefrontand its associated refracted wavefronts, light rays and caustic are computed.We find that the caustic has two branches. The first is constituted by twosegments of a line, one part of this caustic is real and the other one virtual.The second branch of the caustic is a two-dimensional surface with asingularity of the cusp ridge type. It is important to remark that the twobranches of the caustic are disconnected. Because of this property we believethat using this optical element one could generate a scalar opticalaccelerating beam in the region where the caustic is a two-dimensional surfaceof revolution, and at the same time a scalar optical beam with similarproperties to the Bessel beam of zero order in the region were the real causticis a segment of a line along the optical axis.

Wavefronts, light rays and caustic associated with the refraction of a plane wave by a conospherical lens