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

3 

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 $

$\left(S_1 P+P D\right)^2=\left(S_1 S_2\right)^2+\left(S_2 D\right)^2$

Here $S_1 P$ is the path difference $=n \lambda$ for maximum intensity.

∴ $\left(n \lambda+x_{n}\right)^2=(4 \lambda)^2+\left(x_{n}\right)^2$

or $x_n=\frac{16 \lambda^2-n^2 \lambda^2}{2 n \lambda}$

Then $x_1=\frac{16 \lambda^2-\lambda^2}{2 \lambda}=7.5 \lambda$

$x_2=\frac{16 \lambda^2-4 \lambda^2}{4 \lambda}=3 \lambda$

$x_3=\frac{16 \lambda^2-9 \lambda^2}{6 \lambda}=\frac{7}{6} \lambda$

$x_4=0$

∴ Number of points for maxima becomes 3 .