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Pb1-xSrx Te thin films with different strontium (St) compositions are grown on BaF2 (111) substrates by molecular beam epitaxy (MBE). Using high resolution x-ray diffraction (HRXRD), we obtain Pb1-xSrx Te lattice constants,which vary in the range 6.462-6.492 A. According to the Vegard law and HRXRD data, Sr compositions in Pb1-xSrxTe thin films range from 0.0-8.0%. The Pb1-xSrx Te refractive index dispersions are attained from infrared transmission spectrum characterized by Fourier transform infrared (FTIR) transmission spectroscopy.It is found that refractive index decreases while Sr content increases in Pb1-xSrx Te. We also simulate the Pb1-xSrx Te transmission spectra theoretically to obtain the optical band gap energies which range between0.320 e V and 0.449 e V. The simulated results are in good agreement with the FTIR data. Finally, we determine the relation between Ph1-xSrx Te band gap energies and Sr compositions (Eg = 0.320+0.510x- 0.930x2 + 184x3 (e V) ).