  We propose a simple method for determining the redshift $z_{m}$ at which the
angular size of an extragalactic source with fixed proper diameter takes its
minimal value. A closed analytical expression, which is quite convenient for
numerical evaluation is derived. The method is exemplified with the following
FRW type expanding universes: the open matter dominated models
($\Omega_{\Lambda}= 0$), a critical density model with cosmological constant
($\Omega_{\Lambda} \neq 0$), and the class of scalar field cosmologies proposed
by Ratra and Peebles. The influence of systematic evolutionary effects is
briefly discussed.
