when a film of thickness t and refractive index μ is introduced in the path of one of the source of light ,then fringe shift occur as optical path difference changes
Time required by light to reach from S1 to point P where v=c/μ
Hence equivalent path that is covered by light in air is S1P+t(μ-1)
Optical path difference at P
Therefore nth fringe shift is given by
where λ is the wavelength of the wave