To study the optical path difference of a ray passing through a Fourier Transform infrared spectroscopy (FTIR), the symmetric analysis and geometrical optics methods are used to analyze the optical path expression when the ray is passing through one to three plates and a general optical path expression when a ray is passing through arbitrary plates is derived. On the basis of above analysis, the accurate expression of the optical path difference reduced by two arms of a Michelson interferometer with respect to the incident angle is analyzed. Finally, the condition for field widening is given. This research is of great significance to the design of a wide field FTIR.