  We consider a small F=1 spinor condensate inside an optical cavity driven by
an optical probe field, and subject the output of the probe to a homodyne
detection, with the goal of investigating the effect of measurement back-action
on the spin dynamics of the condensate. Using the stochastic master equation
approach, we show that the effect of back-action is sensitive to not only the
measurement strength but also the quantum fluctuation of the spinor condensate.
The same method is also used to estimate the atom numbers below which the
effect of back-action becomes so prominent that extracting spin dynamics from
this cavity-based detection scheme is no longer practical.
