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At O a maximum is observed. Now, u r moving the detector up to X. A MINIMUM is observed at X since the question says no signal is detected here. So what do we know? At minima, the path difference of two waves falling on a point is (n+ 1/2)*lambda, where n is the number of orders of dark fringes. So at X, n=0 so path difference is 1/2*lambda. Hope it helped, dudette (I believe )