Single photon sources are the basis of quantum computing. An optical system including a quantum dot (QD) within the micro-pillar cavity can be a candidate for high quality single photon source. Here, the vacuum Rabi splitting (VRS) of this optical system for different situations was studied. The coupling constant threshold of this Single photon source to start VRS, was calculated for each of these situations. Then, given that the Purcell factor threshold for using single photon source pulses in linear optics quantum computing is, Purcell factor behavior of this single photon source including a QD with FWHM of 5μ eV, was studied. The results showed that to use the single photon pulses of this system in quantum computation ( ), the FWHM of micropillar cavity must be less than 100μ eV. Also, for cavities with normal FWHM range, if coupling constant is greater than 50μ eV, then and therefore its single photons can be used for quantum computing.