The location of the outer caustic β_outer vs. the maximum gradient of the lens potential ﹩{\psi ^{\prime} }_{{\rm{\max }}}﹩. The approximate equivalence of the two quantities indicates that a measurement of β_outer can probe the sharpness of the corresponding IISM structure. Shown are Gaussian (green crosses) and top-hat (blue stars) models with amplitudes A = 10, 10², …, 10⁶ from left to right, respectively. The point mass model also obeys this relation since it has a diverging ﹩{\psi ^{\prime} }_{{\rm{\max }}}﹩ at its center and thus no finite β_outer.