  We use coherence theory to explain why it is necessary to modify the
conventional setup of a Michelson interferometer to obtain Haidinger rings with
an extended source of white light. The modification consists of introducing a
glass slide into one of the two arms of the interferometer. This insertion
circumvents the drastic restriction imposed by the low temporal coherence of
white light, which prevents the observation of interference rings with the
conventional setup. In order to understand this restriction, we developed and
implemented a criterion for observing interference fringes. The modified setup
also makes it possible to perform a spectral interferometry experiment to
analyze the output of the interferometer and determine the refractive index of
the glass slide over the whole visible spectrum. The fit of measured data using
Sellmeier's law gives the extrapolated value of the refractive index to the IR
$n_\mathrm{IR}=1.5307\pm0.0003$ and the value of the characteristic wavelength
$\lambda_0=(164.5\pm0.4)\;\mathrm{nm}$ of the oscillator responsible for the
dispersion.
