A technique for measuring the refractive index of micron sized fibers using a series of immersion index matching oils, and image contrast measurements is proposed and demonstrated. It has been applied to radial silks of the orb web weaving spider Plebs eburnus. These have widths of ∼1-2 microns. Values about 1.5500 are obtained, with birefringence values between 0.0000 and 0.0133 for individual silks. An uncertainty in the range ± 5 × 10 -4 to ± 2 × 10-3 is achieved for these challenging samples. This accuracy is about a twenty times improvement on previously reported measurements for spider silks using other techniques. The technique is used to obtain measurements of the refractive index of spider silks as a function of wavelength, for the first time. An Abbe number for the radial silks of Plebs eburnus of ∼32 is found.