In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at mid-point of screen with $\text{'}\mu \text{'}$ will be best represented by $(\mu \ge 1),$ [Assume slits of equal width and there is no absorption by slab]

A ray of light is incident on a thin film. As shown in figure $M, N$ are two reflected rays and $P,Q$ are two transmitted rays, Rays $N$ and $Q$ undergo a phase change of $\pi .$ Correct ordering of the refracting indices is :

Two point sources separated by $d=5 \mathrm{\mu m}$ emit light of wavelength $\lambda =2 \mathrm{\mu m}$ in phase. A circular wire of radius $20 \mathrm{\mu m}$ is placed around the source as shown in figure.

Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $3\lambda .$ The light is collected on a screen $S$ which is placed at a distance $D(>>\lambda )$ from the slits. The smallest distance $x$ such that the $P$ is a maxima.

In the YDSE shown the two slits are covered with thin sheets having thickness $t \text{\&} 2t$ and refractive index $2\mu$ and $\mu .$ Find the position $\left(y\right)$ of central maxima