Two coherent point sources $A$ and $B$ are at separation $d=\frac{3\lambda }{2},$ where $\lambda$ is wavelength of light emitted by these sources. The oscillations of source $B$ lag in phase behind the oscillations of source $A$ by $\pi .$ The point $P$ is at angular position $\theta$ as indicated in figure. Then

A monochromatic light source $S$, is placed between a mirror and a screen as shown in the figure below,

In YDSE set up one of the slit $S_1$ of a double slit system is wider than the other, so that the amplitude of light reaching the central part of the screen from one slit acting alone is twice that from the other slit acting alone. If $d=4\lambda ,$ maximum value of $\sin \theta$ so that intensity at point $P$ is equal to average intensity on screen
is $\left(\frac{N}{16}\right).$ Find the value of $\mathrm{N}.$

Two coherent point sources of wavelength $\lambda$ are placed at $A$ and $B$ on $x$-axis. The number of minima on $x$-axis is