Two coherent point sources $S_{1}and{S}_2$ vibrating in phase emit light of wavelength  $\lambda$. The separation between the sources is  $3\lambda$. Consider a line passing through  $S_2$ and perpendicular to the line  $S_1{S}_2$. If the smallest distance from $S_2$ where a minimum of intensity occurs is  $\frac{(n+5)\lambda }{20}$, find n