  We show that the usual relation between redshift and angular-diameter
distance can be obtained by considering light from a source to be
gravitationally lensed by material that lies in the telescope beam as it passes
from source to observer through an otherwise empty universe. This derivation
yields an equation for the dependence of angular diameter on redshift in an
inhomogeneous universe. We use this equation to model the distribution of
angular-diameter distance for redshift z=3 in a realistically clustered
cosmology. The distribution is such that attempts to determine q_0 from
angular-diameter distances will systematically underestimate q_0 by ~0.15, and
large samples would be required to beat down the intrinsic dispersion in
measured values of q_0.
