The surface tension of a curved surface behaves differently than that of a planar surface; however, the curvature correction to the surface tension - known as Tolman's length - is commonly ignored in engineering practice. We show that fluid asymmetry, either inherent in binary or ternary systems, or introduced into a pure fluid or a binary fluid by the addition of an impurity, can result in an asymmetric concentration profile and diverging Tolman's length at the critical point. We model the asymmetric two-phase equilibrium in a binary mixture and a ternary mixture using mean-field approximations and the so-called complete scaling approach. The theoretical results are modeled using experimental data for a dilute aqueous near-critical solution of n-hexane (pure fluid with impurity) and for a near-critical binary fluid (methanol-cyclohexane with water as an impurity). The resultant asymmetry parameter will be used to characterize the curvature correction to the interfacial tension of drops and bubbles in the critical region.