Several recent conceptual advances, which take advantage of the polymer conformation in the near critical point of coexisting liquid phases and practical techniques of some unique molecular interactions between polymer chain and the solvent molecules, have been made to allow the investigation of the effect of the well- defined polymer in phase separation of binary mixtures. The behavior of a flexible linear or branched chain polymer (polyethylene oxide, PEO, MW) 9 x 10(5), as an impurity) in the critical binary mixture of isobutyric acid (I) + water (W) was studied by the refractive index (n) measurements using a very accurate and sensitive refractometer. The refractive index in each phase of IW as well as three different PEO concentrations (C = 0.395, 0.796, and 1.605 mg/cm(3)) in the near critical composition of IW have been measured at temperatures below the system's upper critical point. We observed that the polymer was significantly affected in the critical region of IW and these various concentrations of PEO show an important behavior on the critical exponents (beta), the critical temperatures (T-c), and critical composition (phi(c)), which are depicting the shape of the coexistence curve. The phase- transition region of coexisting phases of IW shifts down with the addition of PEO and T-c decreases linearly with increasing PEO concentrations. This may indicate that the polymer chain entangles with each phase, thereby the polymer monomers strongly interact with neighbor solvent particles and also intrachain interaction between the polymer segments. At such conditions, the collapse of polymer chain is possible in the vicinity of the critical point. At temperatures T close enough to T-c, the critical exponent beta (defined by the relation (n(1) - n(2)) proportional to (T-c -T)(beta), with n(1) and n(2) being the refractive indices of the coexisting phases) was found to decrease from 0.382 to 0.360 when the PEO concentration changes from 0.395 to 1.605 mg/cm(3). These values are higher than that of 0.326 +/- 0.005 of pure IW, which is compatible with the three- dimensional Ising value beta = 0.325. The observed critical exponents for the PEO in IW are fully renormalized Ising critical exponents. Besides, the phi(c) values decrease with increasing the C values in the mixture of IW. It appears that the shape of the PEO in IW coexistence curves is similar from that of pure IW.