  We show that a low finesse cavity can be efficient for detecting neutral
atoms. The low finesse can be compensated for by decreasing the mode waist of
the cavity. We have used a near concentric resonator with a beam waist of
12$\mu$m and a finesse of only 1100 to detect magnetically guided Rb atoms with
a detection sensitivity of 0.1 atom in the mode volume. For future experiments
on single atom detection and cavity QED applications, it should be very
beneficial to use miniaturized optical resonator integrated on atom chips.
