In a double slit arrangement,fringes are produced using light of wavelength $4800 \ \mathring A$. One slit is covered by a thin plate of glass of refractive index $1.4$ and the other with another glass plate of the same thickness but of refractive index $1.7$. By doing so,the central bright fringe shifts to the original fifth bright fringe from the center. The thickness of the glass plate is ...... $\mu m$.

$A$ 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.

The fringe widths are found to be $\omega_1$ and $\omega_2$ respectively if a Young's double slit experiment is performed in media of refractive indices $n_1$ and $n_2$ respectively. The correct statement is:

$A$ flake of glass (refractive index $\mu = 1.5$) is placed over one of the openings of a double slit apparatus. The interference pattern displaces itself through seven successive maxima towards the side where the flake is placed. If the wavelength of the light used is $\lambda = 600 \, nm$,then the thickness of the flake is ........ $nm$.

To make the central fringe at the centre $O$,a mica sheet of refractive index $1.5$ is introduced. Choose the correct statement$(s)$.

The slits in a double-slit interference experiment are illuminated by orange light $(\lambda = 600 \ nm)$. $A$ thin transparent plastic sheet of thickness $t$ is placed in front of one of the slits. The number of fringes $(N)$ shifting on the screen is plotted versus the refractive index $\mu$ of the plastic in the graph shown. The value of $t$ is