  We theoretically study the scattering of a plane wave of a ballistic electron
on a circular n-p junction in single and bilayer graphene. We compare the exact
wave function inside the junction to that obtained from a semiclassical formula
developed in catastrophe optics. In the semiclassical picture short-wavelength
electrons are treated as rays of particles that can get reflected and refracted
at the n-p junction according to Snell's law with negative refraction index. We
show that for short wavelength and close to caustics this semiclassical
approximation gives good agreement with the exact results in the case of
single-layer graphene. We also verify the universal scaling laws that govern
the shrinking rate and intensity divergence of caustics in the semiclassical
limit. It is straightforward to generalize our semiclassical method to more
complex geometries, offering a way to efficiently design and model
graphene-based electron-optical systems.
