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

As shown in the figure,in Young's double slit experiment,a thin plate of thickness $t = 10\,\mu m$ and refractive index $\mu_1 = 1.2$ is inserted in front of slit $S_1$. The experiment is conducted in air $(\mu = 1)$ and uses a monochromatic light of wavelength $\lambda = 500\,nm$. Due to the insertion of the plate,the central maxima is shifted by a distance of $x\beta_0$,where $\beta_0$ is the fringe-width before the insertion of the plate. The value of $x$ is $.............$

In Young's double slit experiment, two slits $S_1$ and $S_2$ are $d$ distance apart and the separation from slits to screen is $D$ (as shown in figure). Now, if two transparent slabs of equal thickness $0.1 \, mm$ but refractive indices $1.51$ and $1.55$ are introduced in the path of the beam $(\lambda = 4000 \, \mathring{A})$ from $S_1$ and $S_2$ respectively, the central bright fringe spot will shift by $..........$ number of fringes.

Monochromatic light of wavelength $500 \, nm$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $= 1.5$), the central maximum is shifted to a position previously occupied by the $4^{th}$ bright fringe. The thickness of the glass plate is ..................... $\mu m$.

When a thin plastic film of refractive index $\mu = 1.45$ is placed in the path of one of the interfering waves,the central fringe shifts by a distance equal to $5$ fringes. If the wavelength of light used is $5890 \, \mathring{A}$,find the thickness of the film.

$A$ 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: