Discuss the pattern of interference fringes obtained on the screen away from the two point sources.

Explanation

`S_(1)` and `S_(2)` are two coherent sources and its mid point. At the distance Sto D is the O point on the screen. So is on the perpendicular bisector of `S_(1)S_(2)` so the path difference for each point on it is `S_(1)O = S_(1)O` so central bright fringe form at 0 which will be straight line as shown in figure (a).
In order to determine the shape of the interference pattern on the screen path difference = integer `xx` wavelength then the fringe will be bright and if path difference = odd integer `xx` wavelength then the fringe will be dark.
When `S_(2)P-S_(1)P=(Delta)` is a constant, trajectory of point P on the screen is hyperbola but if the distance between slit to screen is very large the fringes will nearly straight lines. This shown in figures (a) and (b).

Fringe pattern produced by two point source `S_(1)` and `S_(2)` on the screen GG.. Figure (a) and (b) correspond to d = 0.005 mm and d = 0.025 mm, respectively. Both figures correspond to D = 5 cm and `lamda=5xx10^(-5)cm`.