We investigate the cosmological test recently proposed by B. Fort , Y. Mellier and M. Dantel-Fort ( FMD ) , where the observed location of the critical line in gravitational lensing is used to determine the cosmological parameters , \Omega and \lambda .
Applying this method to the cluster of galaxies Cl0024+1654 , FMD obtained a constraint on the cosmological constant , \lambda > 0.6 , assuming the spatially flat universe .
It plays a crucial role in this method that the angular diameter distance-redshift relation depends on the cosmological models through the cosmological parameters .
First , using the angular diameter distance in the Friedmann-Lemaitre-Robertson-Walker universe , we show that one can hardly determine \Omega by this method without the assumption of the spatially flat universe .
We also investigate the effect of inhomogeneities of the universe by using the Dyer-Roeder angular diameter distance .
It is shown that the effect of inhomogeneities can become too large to be ignored , particularly for a high density universe .
As a result , this method can not be taken as a clear cosmological test to determine \Omega and \lambda , though it may provide a bound on \Omega and \lambda .
Moreover , we mention the uncertainty of the determination of the velocity dispersion , which is regarded as one of the most serious problems in this test .