Fig. shows a modified Y.D.S experimental set up. Here S is not symmetrically placed with respect to S1 and S2 . Due to this there is an intial path difference Δi between S1 and S2 .
Δi = SS1 - SS2
We can also say there is an initial phase difference δi
between S1 and S2 . Obviously δi = 2π/λ Δi . The total path
difference ΔT at any point P on screen is
The condition for constructive and distructive interference is
Constructive interference
Destructive interference
The centeral maximum is not located at O. Let y0 be the position of central maximum. Putting n = 0; from Eqn. (1) we have
The negative sign shows that centeral fringe is below point O. If in the modified set up SS2 > SS1 the centeral fringe shifts above point O. The fringe width β , however remains same.
Let a thin film of thickness t; refractive index μ be introduced is the path of one of the two interferring beams; say S1P; in standard Young’s double slit experiment. The path difference, Δ' , between the two disturbances at point P is
A thickness t of film is equivalent to a path μt in air. Therefore,
This a change (μ - 1)t in the path difference. Due to this the fringe pattern shifts but β remains same. For constructive interference
The centeral fringe shift from O by a distance y0 . yo is obtained by putting n = 0 in Eqn. (5). Therefore
Let Δn be the fringe shift. Then
