  The aim of the present work is to introduce a lens whose faces are a conical
surface and a spherical surface. We illuminate this lens by a plane wavefront
and its associated refracted wavefronts, light rays and caustic are computed.
We find that the caustic has two branches. The first is constituted by two
segments 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 a
singularity of the cusp ridge type. It is important to remark that the two
branches of the caustic are disconnected. Because of this property we believe
that using this optical element one could generate a scalar optical
accelerating beam in the region where the caustic is a two-dimensional surface
of revolution, and at the same time a scalar optical beam with similar
properties to the Bessel beam of zero order in the region were the real caustic
is a segment of a line along the optical axis.
