Relation between the mid-IR spectral index α and the radial dust distribution power law index a in type 1 AGN. Model points are shown for all combinations of N₀ = 2.5, 5, 7.5, and 10 (color-coded symbols) and half-opening angle 30° (squares), 45° (circles), and 60° (diamonds) for both spherical (bluish-colored symbols) and cylindrical (reddish-colored symbols) vertical distributions. In order to cover a range of type-1 inclinations, results for i = 0° (face-on; upward offset), i = 15° (nominal a value) and i = 30° (downward offset) are presented for all a-values. The black-filled circles with errors denote the nominal α-value for each a and one standard deviation. The nominal fit using all values (solid black line) has a slope of  −0.93 and a Spearman rank correlation of  −0.97. Fits using only results with half-opening angle 30° (dash-dotted line), 45° (dashed line; almost coincident with the solid line), and 60° (dotted line) are also shown for illustration.