Two coherent sources, S1 and S2 lie along the y-axis and a detector moves along +x-axis. The sources are separated by a distance four times the wavelength λ of the source. Find the number of points where maxima are observed, leaving the origin and far-off points.

In ΔS1S2D, from pythagoras theorem we can write S1D2=S1S22+S1D2S1P+PD2=S1S22+S2D2Here S1 P is the path difference at point D from the two sources. For maximum intensity at point D it should be = nλ. LetPD=S2D=xn. Then,nλ+xn2=(4λ)2+xn2or xn=16λ2−n2λ22nλThen x1=16λ2−λ22λ=7.5λx2=16λ2−4λ24λ=3λx3=16λ2−9λ26λ=76λx4=0Thus number of points for maxima are 3.