  In this work we compute the resonant wavelength of whispering gallery modes
for bulk-fused silica microspheres including chromatic dispersion. This is done
following two methods: by solving the exact characteristic equation and, on the
other hand, by solving the nonlinear equations that result for a variable
refractive index in the asymptotic approximations. Similar results with both
methods are obtained with differences below $1\%$ . Nevertheless, important
differences are found with respect to the resonant wavelengths computed with a
constant index and with a variable index. We compute the free spectral range
and the quality factor, and make a comparison between the variable index and
the constant index cases. The differences are of significant relevance for the
free spectral range, while for the quality factor, the constant case is
insensitive to the chromatic dispersion. Our work could be useful as a pathway
for designing microspheres for different applications.
