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?

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:

$A$ monochromatic beam of light falls on a $YDSE$ apparatus at an angle $\theta$ as shown in the figure. $A$ thin sheet of glass of thickness $t$ and refractive index $\mu$ is inserted in front of the lower slit $S_2$. The central bright fringe (path difference $= 0$) will be obtained:

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 a Young's double slit experiment with light of wavelength $\lambda ,$ the fringe pattern on the screen has a fringe width $\beta .$ When two thin transparent glass (refractive index $\mu$) plates of thickness $t_1$ and $t_2$ $(t_1 > t_2)$ are placed in the path of the two beams respectively,the fringe pattern will shift by a distance:

In $YDSE$,the source $S$ placed symmetrically with respect to the slits $S_1$ and $S_2$ is now moved parallel to the plane of the slits so that it is closer to the upper slit $S_1$,as shown. Then,