What happens to the interference pattern when two coherent sources are (a) infinitely close, and (b) far apart from each other

(a) When ' \(\displaystyle d\) ' is very small, \(\displaystyle \beta \propto \frac{1}{d}, \beta\) will be very large and a single patch will occupy the whole field of view hence pattern cannot be observed.

(b) When sources are far apart, i.e \(\displaystyle d\) is very large, then fringe width will be so small that the fringes are not resolved and cannot be seen separately.