Refractive index dispersion causes the light line to curve. As a result it is shown that when the prism is dispersive, an additional dip in the spectral response of Surface Plasmon Resonance (SPR) sensors is observed in the Kretschmann-Raether (KR) configuration. Since the new dip evolves in the infrared (IR) region, it exhibits a high sensitivity to the analyte refractive index (RI) changes and the mode penetrates deeper into the analyte. Adding a thin dielectric layer with high refractive index on top of the metallic layer enables to control the dip location and strength. The two dips shift in opposite directions as the analyte RI changes and therefore when the spectral difference is considered as the measurand, higher RI sensitivity is obtained. The dispersion relation of two thin films bounded by two semi-infinite media is derived when the prism dispersion is considered.