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

(N/A) $S_{1}$ and $S_{2}$ are two coherent sources and $S$ is their midpoint. The point $O$ on the screen is at a distance $D$ from $S$. Since $SO$ lies on the perpendicular bisector of $S_{1}S_{2}$, the path difference for any point on this line is $S_{1}O = S_{2}O$. Therefore, a central bright fringe forms at $O$, which appears as a straight line as shown in figure $(a)$.
To determine the shape of the interference pattern on the screen, we use the condition that if path difference $= n\lambda$ (where $n$ is an integer), the fringe is bright, and if path difference $= (2n+1)\lambda/2$ (where $n$ is an integer), the fringe is dark.
When $S_{2}P - S_{1}P = \Delta$ is a constant, the trajectory of point $P$ on the screen is a hyperbola. However, if the distance between the slits and the screen $(D)$ is very large, the fringes appear as nearly straight lines. This is shown in figures $(a)$ and $(b)$.
The fringe patterns produced by two point sources $S_{1}$ and $S_{2}$ on the screen are shown. Figures $(a)$ and $(b)$ correspond to $d = 0.005 \text{ mm}$ and $d = 0.025 \text{ mm}$, respectively, with $D = 5 \text{ cm}$ and $\lambda = 5 \times 10^{-5} \text{ cm}$.
In the double-slit experiment, we assumed the source $S$ is on the perpendicular bisector of the two slits. If the source $S$ is moved to a new point $S^{\prime}$ away from the perpendicular bisector, the interference pattern shifts accordingly.