The binary liquid phase separation of aqueous solutions of gamma-crystallins is utilized to gain insight into the microscopic interactions between these proteins. The interactions are modeled by a square-well potential with reduced range lambda and depth epsilon. A comparison is made between the experimentally determined phase diagram and the results of a modified Monte Carlo procedure which combines simulations with analytic techniques. The simplicity and economy of the procedure make it practical to investigate the effect on the phase diagram of an essentially continuous variation of lambda in the domain 1.05 less than or equal to lambda less than or equal to 2.40. The coexistence curves are calculated and are in good agreement with the information available from previous standard Monte Carlo simulations conducted at a few specific values of X. Analysis of the experimental data for the critical volume fractions of the gamma-crystallins permits the determination of the actual range of interaction appropriate for these proteins. A comparison of the experimental and calculated widths of the coexistence curves suggests a significant contribution from anisotropy in the real interaction potential of the gamma-crystallins. The dependence of the critical volume fraction phi(c) and the reduced critical energy <(epsilon)over cap>(c) upon the reduced range lambda is also analyzed in the context of two "limiting" cases; mean field theory (lambda --> infinity) and the Baxter adhesive sphere model (lambda --> 1). Mean field theory fails to describe both the value of phi(c) and the width of the coexistence curve of the gamma-crystallins. This is consistent with the observation that mean field is no longer applicable when lambda less than or equal to 1.65. In the opposite case, lambda --> 1, the critical parameters are obtained for ranges much shorter than those investigated in the literature. This allows a reliable determination of the critical volume fraction in the adhesive sphere limit, phi(c)(lambda = 1) = 0.266 +/- 0.009.