6. An interference is observed due to two coherent sources 'A' and 'B' having phase constant zero separated by a distance 4 λ  along the y-axis where  λ  is the wavelength of the source . A detector D is moved on the positive x-axis. The number of points on the x-axis excluding the points x=0 & x=  at which maximum will be observed is,
(A) three
(B) four 
(C) two
(D) infinite

Dear Student,

Let BD =x n
For maximum intensity,
AD-BD=nλ

or AD=nλ+xnFrom figure,AD2=(AB)2+(BD)2(nλ+xn)2=(4λ)2+x2nsolving for xn we havexn=16λ2-n2λ22nλwhen n=1x1=16λ2-λ22λ=7.5λsimilarly when n=2x2=3λand when n=3x3=76λso the number of points at which maximum will be observed is 3.

Regards

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