Explanation

(b) From $\Delta S_{1}S_{2}D$,
$\left( S_{1}D \right)^{2} = \left( S_{1}S_{2} \right)^{2} + \left( S_{2}D \right)^{2}$
$\left( S_{1}P + PD \right)^{2} = \left( S_{1}S_{2} \right)^{2} + \left( S_{2}D \right)^{2}$
Here $S_{1}P$ is the path difference $= n\lambda$ for maximum intensity
$\therefore\left( n\lambda + x_{n} \right)^{2} = (4\lambda)^{2} + \left( x_{n} \right)^{2}$
Or $x_{n} = \frac{16\lambda^{2} - n^{2}\lambda^{2}}{2n\lambda}$
Then $x_{1} = \frac{16\lambda^{2} - \lambda^{2}}{2\lambda} = 7.5\lambda$
$x_{2} = \frac{16\lambda^{2} - 4\lambda^{2}}{4\lambda} = 3\lambda$
$x_{3} = \frac{16\lambda^{2} - 9\lambda^{2}}{6\lambda} = \frac{7}{6}\lambda$
$x_{4} = 0$
$\therefore$ Number of points for maxima becomes 3