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We investigate the cosmological test recently proposed by B. Fort, Y. Mellierand M. Dantel-Fort (FMD), where the observed location of the critical line ingravitational lensing is used to determine the cosmological parameters,$\Omega$ and $\lambda$. Applying this method to the cluster of galaxiesCl0024+1654, FMD obtained a constraint on the cosmological constant, $\lambda >0.6$, assuming the spatially flat universe. It plays a crucial role in thismethod that the angular diameter distance-redshift relation depends on thecosmological models through the cosmological parameters. First, using theangular diameter distance in the Friedmann-Lemaitre- Robertson-Walker universe,we show that one can hardly determine $\Omega$ by this method without theassumption of the spatially flat universe. We also investigate the effect ofinhomogeneities of the universe by using the Dyer-Roeder angular diameterdistance. It is shown that the effect of inhomogeneities can become too largeto be ignored, particularly for a high density universe. As a result, thismethod cannot 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.Comment: 16 pages, LaTeX(aaspp4), 11 postscript figures included; submitted to  The Astrophysical Journa

Critical Lines in Gravitational Lenses and the Determination of Cosmological Parameters