Monochromatic  light  (single  wavelength)  falls  on  two  narrow  slits S1and S2 which  are  very  close together   acts   as   two   coherent   sources,   when   waves   coming   from two   coherent   sources s1 and s2 superimposes  on  each  other,  an  interference  pattern  is  obtained  on  the  screen.In YDSE alternate bright and dark bands obtained on the screen.these bands are called fringes.

When a film of thickness’t’ and refractive index 'm' is introduced in the path of one of the sources, then fringe shift occurs as the optical path difference changes.

Optical path difference changes

Optical path difference at

P = S2P - [S1P+ µt - t] = S2P - S1P - (µ - 1)t = y.d/D - (µ - 1)

⇒  nth fringe is shifted by  Δy = D(µ-1)t/d = w/λ (µ-1)t