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Refractive index is an optical property explored in the light scattering measurement of micro- and nano-particles as well as in label-free imaging of cells and tissues. Because the refractive index value is a major input to the characterization and quantification of the analyzed specimens, various methods have been developed targeting at different sample types. In this paper, we demonstrate a technique for the refractive index measurement of homogeneous microspheres and liquids in the short-wave infrared (SWIR) range. We use synthetic phase microscopy (SPM), which records a scattering-corrected projection of the 3D refractive index distribution, in combination with a least-squares fitting to a theoretical model of a sphere. Using the method, we determine the refractive index dispersion of two polymer microspheres (polymethyl methacrylate and polystyrene), two glass microspheres (silica and soda lime), and three microscopy mounting media (glycerol, FluorSave, and Eukitt) in the SWIR range of 1100–1650 nm.