  Propagation of light in a clumpy universe is examined. As an inhomogeneous
matter distribution, we take a spherical void surrounded by a dust shell where
the ``lost mass'' in the void is compensated by the shell. We study how the
angular-diameter distance behaves when such a structure exists. The
angular-diameter distance is calculated by integrating the Raychaudhuri
equation including the shear. An explicit expression for the junction condition
for the massive thin shell is calculated. We apply these results to a dust
shell embedded in a Friedmann universe and determine how the distance-redshift
relation is modified compared with that in the purely Friedmann universe. We
also study the distribution of distances in a universe filled with voids. We
show that the void-filled universe gives a larger distance than the FRW
universe by $\sim 5%$ at $z \sim 1$ if the size of the void is $\sim 5%$ of the
Horizon radius.

Astrophysics