Two coherent sources S₁ and S₂ are separated by a distance four times the wavelength $\lambda$ of the source. The sources lie along y axis with one at the origin .A detector moves along + x axis. Leaving the origin and far off points the number of points where maxima are observed is

$$\begin{gathered} From \Delta S_1{S}_{2}D, \\ {\left(S_{1}D\right)}^2={\left(S_1{S}_2\right)}^2+{\left(S_{2}D\right)}^2 \\ \Rightarrow {(S_{1}P+PD)}^2={\left(S_1{S}_2\right)}^2+{\left(S_{2}D\right)}^2 \\ Here S_{1}P is the path difference =n\lambda [for maximum intensity] \\ \therefore {(n\lambda +x_n)}^2={\left(4\lambda \right)}^2+{\left(x_n\right)}^2 \\ or x_n=\frac{16{\lambda }^2-n^2{\lambda }^2}{2n\lambda } \\ Then, x_1=\frac{16{\lambda }^2-{\lambda }^2}{2\lambda }=7.5\lambda \\ {x}_2=\frac{16{\lambda }^2-4{\lambda }^2}{4\lambda }=3\lambda \\ {x}_3=\frac{16{\lambda }^2-9{\lambda }^2}{6\lambda }=\frac{7}{6}\lambda \\ {x}_4=0 \\ Hence, Number of points for maxima becomes 3 \end{gathered}$$