The measurement of the refractive index of optical glass samples is a common and fundamental activity in numerous fields of expertise. Several measurement techniques exist with relative accuracies from ^{10  −  2} to, at least, ^{10  −  7} with complexities that are inversely related to the corresponding uncertainty. We describe an implementation of a technique based on the measurement of the lateral displacement variation of a collimated beam caused by the rotation of a parallel plate glass sample. The method was aimed to achieve an uncertainty in the range from ^{10  −  3} to ^{10  −  4} without increasing the complexity normally associated with techniques with this level of accuracy. The system was designed and optimized based on a detailed analysis of the uncertainty budget. We describe the implementation, the data processing, and the results obtained with calibrated samples, showing a relative uncertainty at the level of ^{10  −  4}.