We propose and evaluate a spectroscopic refractometer device to measure the refractive index dispersion of transparent and absorbing solutions. The angle-dependent reflectivity of a white beam of light in an internal reflection configuration around the critical angle is spectrally analyzed. The refractive index in a wavelength range from 400 nm to 900 nm is obtained from the angle-reflectivity curve around the critical angle at each wavelength. The device does not use angle scanning mechanisms, decreasing considerably the complexity of the instrument in comparison to previous proposals. As a result, the measurements are obtained relatively fast. Nevertheless, a good experimental resolution in refractive index of about Δn ≈ 10(-4) at all the wavelengths is achieved in the case of transparent solutions. The calibration procedure of the device is discussed in detail. We also present measurements of the refractive index dispersion of rhodamine 6G-methanol solutions, which has a strong absorption band in the visible spectra.