Mountain shadows revisited

Using purely geometric considerations, a sequence of mountain shadow models is considered. The observer is located at the summit of idealized mountains with several different cross-sectional profiles. The result for a triangular profile is generalized to the case of an off-summit observer. We also examine the case of a conical mountain. In addition, a simple geometric model is formulated for mountain "spikes" in terms of the differences in shadow length and contrast for an off-summit observer within the shadow. The first appendix is devoted to the notion of "umbral volume" and the second to the geometry of sunlit areas on a conical mountain.