A first accurate measurement of the complex refractive index in an intralipid emulsion is demonstrated, and thereby the average scatterer particle size using standard Mie scattering calculations is extracted. Our method is based on measurement and modeling of the reflectance of a divergent laser beam from the sample surface. In the absence of any definitive reference data for the complex refractive index or particle size in highly turbid intralipid emulsions, we base our claim of accuracy on the fact that our work offers several critically important advantages over previously reported attempts. First, our measurements are in situ in the sense that they do not require any sample dilution, thus eliminating dilution errors. Second, our theoretical model does not employ any fitting parameters other than the two quantities we seek to determine, i.e., the real and imaginary parts of the refractive index, thus eliminating ambiguities arising from multiple extraneous fitting parameters. Third, we fit the entire reflectance-versus-incident-angle data curve instead of focusing on only the critical angle region, which is just a small subset of the data. Finally, despite our use of highly scattering opaque samples, our experiment uniquely satisfies a key assumption behind the Mie scattering formalism, namely, no multiple scattering occurs. Further proof of our method's validity is given by the fact that our measured particle size finds good agreement with the value obtained by dynamic light scattering.