Using a complete, magnitude-limited sample of active galaxies from the Sloan
Digital Sky Survey (SDSS) we show that the fraction of broad-line (Type 1)
active galactic nuclei increases with luminosity of the isotropically-emitted
[O III] narrow emission line. Our results are quantitatively in agreement with,
and far less uncertain than, similar trends found from studies of X-ray and
radio-selected active galaxies. While the correlation between broad-line
fraction and luminosity is qualitatively consistent with the receding torus
model, its slope is shallower and we therefore propose a modification to this
model where the height of the torus increases slowly with AGN luminosity. We
demonstrate that the faint-end slope of the AGN luminosity function steepens
significantly when a correction for `missing' Type 2 objects is made and that
this can substantially affect the overall AGN luminosity density extrapolated
from samples of more luminous objects.Comment: 8 pages, accepted for publication by MNRA