The liquid liquid coexistence curves of the binary solutions of 1-buty1-3-methylimidazolium tetrafluoroborate ([C(4)mim][BF(4)]) + 1,3-propanediol and [C(4)mim][BF(4)] + 1,4-butanediol were determined by measuring the temperature dependence of the refractive index in the two phases of the samples with critical compositions. The critical amplitude 13 and the critical exponent beta have been deduced from the coexistence curves. The experimental values of beta are consistent with theoretical prediction. The results have also been analyzed to determine the Wegner-correction terms and to examine the asymmetric behavior of the diameters of the coexistence curves.