A cloud of atoms reflecting from an evanescent-wave mirror produces a
phase shift on the beam producing the evanescent wave. This shift can
be used to detect the passage of the atoms. We give a physical discuss
ion of this process and estimate the phase shift. The shift can be gre
atly increased by using a resonant planar waveguide. We also estimate
the signal-to-noise ratio and show how to optimize the experimental pa
rameters of such a measurement. Using the waveguide we find a-signal-t
o-noise ratio of order of 300 in a realistic experimental situation.