In a Young's double-slit experiment,let $A$ and $B$ be the two slits. $A$ thin film of thickness $t$ and refractive index $\mu$ is placed in front of $A$. Let $\beta =$ fringe width. The central maximum will shift:

$A$ thin mica sheet of thickness $2 \times 10^{-6} \ m$ and refractive index $\mu = 1.5$ is introduced in the path of the first wave. The wavelength of the wave used is $5000 \ \mathring{A}$. The central bright maximum will shift:

$A$ 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 the given figure,light is incident at an angle $\theta$ with the normal to a plane containing two slits of separation $d$. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle $\theta$ and outgoing angle $\phi$.

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 ...... $\mu m$.

Young's double slit experiment is conducted in a liquid of refractive index $\mu_1$ as shown in the figure. $A$ thin transparent slab of refractive index $\mu_2$ and thickness $t$ is placed in front of the slit $S_2$. The magnitude of the optical path difference at point $O$ is