A general formulae of signal intensity on time delay four wave mixing with incoherent light (TDFWM IL) is deduced based on two level model. The result shows that signal intensity in TDFWM IL is symmetric for linewidth limited light beams, the signal peak is proportional to the linewidth of excitation beams and inversely proportional to longitudinal relaxation rate. The result is applicable to the study of ultrafast dynamitic process in semiconductor optical amplifier (SOA) and active light waveguide. Furthermore, an effective experimental scheme based on the TDFWM IL structure of LED is proposed for the observation of inter and intra band carrier relaxation rates in the active medium.