  We demonstrate for a passive optical cavity containing a dispersive atomic
medium, the increase in scale factor near the critical anomalous dispersion is
not cancelled by mode broadening or attenuation, resulting in an overall
increase in the predicted quantum-noise-limited sensitivity. Enhancements of
over two orders of magnitude are measured in the scale factor, which translates
to greater than an order-of-magnitude enhancement in the predicted
quantum-noise-limited measurement precision, by temperature tuning a
low-pressure vapor of non-interacting atoms in a low-finesse cavity close to
the critical anomalous dispersion condition. The predicted enhancement in
sensitivity is confirmed through Monte-Carlo numerical simulations.
