In a double slit experiment,the distance between the slits is $0.1 \ cm$ and the screen is placed at $50 \ cm$ from the slits plane. When one slit is covered with a transparent sheet having thickness $t$ and refractive index $n = 1.5$,the central fringe shifts by $0.2 \ cm$. The value of $t$ is . . . . . . $cm$.

The central fringe of the interference pattern produced by light of wavelength $6000 \mathring A$ is found to shift to the position of the $4^{\text {th}}$ bright fringe after a glass plate of refractive index $1.5$ is introduced in front of one slit in Young's experiment. The thickness of the glass plate will be ......... $\mu m$.

To make the central fringe appear at the centre $O,$ a mica sheet of refractive index $\mu = 1.5$ is introduced. Choose the correct statement:

In Young's double slit experiment, the aperture screen distance is $2 \, m$. The fringe width is $1 \, mm$. Light of $600 \, nm$ is used. If a thin plate of glass $(\mu = 1.5)$ of thickness $0.06 \, mm$ is placed over one of the slits, then there will be a lateral displacement of the fringes by $... \, cm$.

$A$ 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 double-slit experiment,instead of taking slits of equal widths,one slit is made twice as wide as the other. Then,in the interference pattern: