Consider a gravitational lens system with K planes. If light rays are traced back from the observer to the light source plane, then the points on the first lens plane where a light ray either terminates, or, passes through and terminates before reaching the light source plane, are “obstruction points.” More precisely, tracing rays back to the source plane induces a K-plane lensing map η : U ⊆ R 2 → R 2 of the form η(x 1) = x 1 −∑i=1 k αi (x i (x i )). We then define an obstruction point of η to be a point a of U where limx1→a |αi (x i (x 1))| = ∞ for some “deflection angle” αi .