$A$ thin glass plate of thickness $t = \frac{2500}{3} \lambda$ (where $\lambda$ is the wavelength of light used) and refractive index $\mu = 1.5$ is inserted between one of the slits and the screen in Young's double slit experiment. At a point on the screen equidistant from the slits,the ratio of the intensities before and after the introduction of the glass plate is

In Young's double slit experiment,a glass plate is placed before one slit which absorbs half the intensity of light. Under this case:

In a Young's double-slit experiment,a thin plate of thickness $2 \times 10^{-6} \ m$ and refractive index $\mu = 1.5$ is placed in the path of one of the slits. By how many fringe widths does the central bright fringe shift? The wavelength of the light used is $5000 \ \mathring{A}$.

While conducting the Young's double slit experiment,a student replaced the two slits with a large opaque plate in the $x-y$ plane containing two small holes that act as two coherent point sources $(S_1, S_2)$ emitting light of wavelength $600 \ nm$. The student mistakenly placed the screen parallel to the $x-z$ plane (for $z>0$) at a distance $D=3 \ m$ from the mid-point of $S_1 S_2$,as shown schematically in the figure. The distance between the sources $d=0.6003 \ mm$. The origin $O$ is at the intersection of the screen and the line joining $S_1 S_2$. Which of the following is(are) true of the intensity pattern on the screen?
$(A)$ Straight bright and dark bands parallel to the $x$-axis
$(B)$ The region very close to the point $O$ will be dark
$(C)$ Hyperbolic bright and dark bands with foci symmetrically placed about $O$ in the $x$-direction
$(D)$ Semi circular bright and dark bands centered at point $O$

In Young's double-slit experiment,a mica sheet of refractive index $\mu$ and thickness $t$ is introduced in the path of the light ray from the first source $S_1$. By what distance will the fringe pattern be shifted?

$A$ 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.