In a Young's double-slit experiment,light of wavelength $4800 \, \mathring{A}$ is used. One slit is covered by a thin transparent plate of refractive index $1.4$ and the other slit is covered by another thin transparent plate of refractive index $1.7$. As a result,the central bright fringe shifts to the position where the fifth bright fringe was previously formed. If the thickness of both plates is the same,find the thickness in $\mu m$.

$A$ double slit setup is shown in the figure. One of the slits is in medium $2$ of refractive index $n_2$. The other slit is at the interface of this medium with another medium $1$ of refractive index $n_1(\neq n_2)$. The line joining the slits is perpendicular to the interface and the distance between the slits is $d$. The slit widths are much smaller than $d$. $A$ monochromatic parallel beam of light is incident on the slits from medium $1$. $A$ detector is placed in medium $2$ at a large distance from the slits,and at an angle $\theta$ from the line joining them,so that $\theta$ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.
Which of the following statement$(s)$ is (are) correct?
$(A)$ The phase difference between the two rays is independent of $d$.
$(B)$ The two rays interfere constructively at the detector.
$(C)$ The phase difference between the two rays depends on $n_1$ but is independent of $n_2$.
$(D)$ The phase difference between the two rays vanishes only for certain values of $d$ and the angle of incidence of the beam,with $\theta$ being the corresponding angle of refraction.

In a Young's double slit experimental arrangement shown here,if a mica sheet of thickness $t$ and refractive index $\mu$ is placed in front of the slit $S_1$,then the path difference $(S_1P - S_2P)$

In the $YDSE$ shown,the two slits are covered with thin sheets having thickness $t$ and $2t$,and refractive index $2\mu$ and $\mu$ respectively. Find the position $(y)$ of the central maxima.

In Young's double-slit experiment,if one slit is made twice as wide as the other instead of having equal widths,then in the interference pattern:

$A$ monochromatic light source $S$ of wavelength $440 \,nm$ is placed slightly above a plane mirror $M$ as shown below. The image of $S$ in $M$ can be used as a virtual source to produce interference fringes on the screen. The distance of source $S$ from $O$ is $20.0 \,cm$ and the distance of the screen from $O$ is $100.0 \,cm$ (figure is not to scale). If the angle $\theta = 0.50 \times 10^{-3} \,radians$, then the width of the interference fringes observed on the screen is ............... $mm$.