Two coherent point sources  S1 and S2 vibrating in phase emit light of wavelength  λ. The separation between the sources is 2λ. The smallest distance from S2 on a line passing through  S2 and perpendicular to  S1,S2, where a minimum of intensity occurs is:

[Concept]: Path difference at S2 is 2λ. Therefore for minimum intensity(dark band) at P.[Step 1]:  For Dark band:path difference  Δx=2n−12λ​S1P−S2P=3λ2..........i[Step 2]:  4λ2+x2−x=3λ2[Step 3]: ⇒4λ2+x2=x+3λ2​squaring on both sides​⇒4λ2+x22=x+3λ22​⇒4λ2+x2=x2+3λ22+2x3λ2​⇒4λ2−9λ24=3xλ​⇒16−9λ24=3xλ     Solving equation, x=7λ12