No interference pattern is detected when two coherent sources are infinitely close to each other. Why?
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Fringe width of interference fringes is given by $\beta=\frac{\text{D}\lambda}{\text{d}}\alpha\frac{1}{\text{d}}.$ When d is infinitely small, fringe width β will be too large. In such a case even a single fringe may occupy the whole field of view. Hence, the interference pattern cannot be detected.
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