  Lensed billiards are an extension of the notion of billiard dynamical systems
obtained by adding a potential function of the form $C1_{\mathcal{A}}$, where
$C$ is a real valued constant and $1_{\mathcal{A}}$ is the indicator function
of an open subset $\mathcal{A}$ of the billiard table whose boundaries (of
$\mathcal{A}$ and the table) are piecewise smooth. Trajectories are polygonal
lines that undergo either reflection or refraction at the boundary of
$\mathcal{A}$ depending on the angle of incidence. After laying out some basic
concepts and general facts, in particular reviewing the optical/mechanical
analogy that motivates these billiard models, we explore how their dynamical
properties depend on the potential parameter $C$ using a number of families of
examples. In particular, we explore numerically the Lyapunov exponents for
these parametric families and highlight the more salient common properties that
distinguish them from standard billiard systems. We further justify some of
these properties by characterizing lensed billiards in terms of switching
dynamics between two open (standard) billiard subsystems and obtaining mean
values associated to orbit sojourn in each subsystem.
