Interferometric measurements of the effect of a polymer gradativelly added in a lyotropic liquid crystal is reported here. Studies of the phase diagram, birefringence and critical exponents as a function of the polymer concentration are presented. Measurements of the optical birefringence as a function of temperature are performed with the micellar system potassium laurate, l-decanol, and water doped with variable quantities of the polymer poly-ethylene-glycol (PEG). The transitions from the calamitic nematic phase to a reentrant discotic-biaxial-discotic phase were observed when increasing the PEG molar concentration. Our results confirm the critical properties of the uniaxial-to-biaxial nematic transition. The critical exponent for the order parameter (beta = 0.38) obtained for the sample without PEG is in good agreement with the value calculated for the XY model. Some results with higher PEG doping concentration indicate that beta is higher than 0.38 leading to the mean-field value.