A model is presented for the effect of a finite extinction ratio of the light modulator used in continuous wave cavity ring-down spectroscopy (CW-CRDS) experiments. We present a simple analytical expression for the minimum isolation required to prevent a significant increase in the fluctuations of the cavity decay rate, which determine the sensitivity of the method. We also present systematic measurements of the signal to noise in CW-CRDS as a function of the effective isolation of the light modulator, and excellent agreement with the model is found.