In this Letter, we demonstrate the possibility to measure the refractive index of a liquid, using the stimulating Brillouin scattering in a 3-cm-long side-polished optical fiber. In addition, we show that by depositing a high-refractive index layer on the polished surface the sensitivity of the Brillouin frequency shift (BFS) can be increased due to a higher penetration of the evanescent field in the outer medium. Experiments show a maximum BFS change of about 11 MHz when varying the refractive index of the external medium from 1 (air) to 1.402, and a BFS sensitivity to refractive index of about 293 MHz/RIU around 1.40.