We report the measurements of birefringence as a function of temperature of a binary system 4-cyanophenyl [4'(4''-n-heptylphenyl)]benzoate (7CPB) + 4-cyanophenyl 4-nonylbenzoate (9.CN) showing a nematic-smectic A(d)-re-entrant nematic phase sequence by means of the optical transmission method. The temperature dependence of the birefringence has been determined from the transmitted intensity data and the orientational order parameters have been calculated. These observations indicate that re-entrant nematic to induced smectic A(d) and induced smectic A(d) to nematic phase transitions for all the mixtures are of second order. There is a continuous change in the Δn values at the nematic-smectic A(d) and smectic A(d)-re-entrant nematic phase transitions. However, for some mixtures a slight increase in birefringence on cooling in the vicinity of the smectic A(d)-re-entrant nematic transition has been observed. We have also fitted our experimental results with those calculated from the modified McMillan theory as proposed by Luckhurst and Timimi.