  Long cylinders, such as optical fibers, are some of the most widely used
photonic devices. The radius and refractive index of these fibers are therefore
fundamentally important parameters in determining their performance. We have
developed a method to determine the absolute radius, refractive index, and
chromatic dispersion of a long cylinder using only the resonance wavelengths of
the whispering gallery modes around its circumference for two different
polarizations. Since this method only requires the measurement of resonance
wavelengths, it is non-destructive and it can be performed using standard
equipment. As a proof-of-concept, we demonstrate the method on a $125\mu m$
optical fiber and an $80\mu m$ borosilicate capillary fiber with thick walls,
obtaining values for the diameter and the refractive index with an accuracy of
$2 nm$ and $2\times 10^{-5}$, respectively.
