Consider the arrangement shown in the figure. By some mechanism, the separation between the slits $S_3$ and $S_4$ can be changed. The intensity is measured at the

 

point $\mathrm{P}$ which is at the common perpendicular bisector of $S_1{S}_2$ and $S_3{S}_4.$ When $z=\frac{D\mathrm{\lambda }}{2d},$ the intensity measured at $P$ is $I.$ Find this intensity when $z$ is equal to,

(a) $\frac{D\mathrm{\lambda }}{d}$,

(b) $\frac{3D\mathrm{\lambda }}{2d}$ and
(c) $\frac{2D\mathrm{\lambda }}{d}$.