For the sake of completeness, we include the case of a *concave* simple lens, shown in Figure 4.15. Parallel rays are forced to diverge, rather than converge; however, a meaningful notion of negative focal length exists by tracing the diverging rays backwards through the lens. The Lensmaker's Equation (4.7) can be slightly adapted to calculate negative in this case [105].

Steven M LaValle 2020-01-06