In a double slit experiment,when one of the slits is covered by a transparent mica sheet of refractive index $1.56$,the central fringe shifts to the position of $7^{th}$ bright fringe,obtained with both slits uncovered. If the light source wavelength is $450 \text{ nm}$,the thickness of mica sheet is $\alpha \times 10^{-9} \text{ m}$. The value of $\alpha$ is . . . . . . .

$A$ small transparent slab of refractive index $\mu = 1.5$ and thickness $L = d/4$ is placed along the path $AS_2$ (see figure). What will be the distance from $O$ of the principal maxima and the first minima on either side of the principal maxima obtained in the absence of the glass slab? Given $AC = CD = D$ and $S_1C = S_2C = d$ (where $d << D$).

The central fringe of an interference pattern produced by light of wavelength $6000 \, \mathring{A}$ is found to shift to the position of the fourth bright fringe after a glass plate of refractive index $1.5$ is introduced in front of one slit. The thickness of the glass plate would be ...... $\mu m$.

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.

In a Young's double-slit experiment,light of wavelength $4800 \, \mathring{A}$ is used. One slit is covered by a thin transparent plate of refractive index $1.4$ and the other slit is covered by another thin transparent plate of refractive index $1.7$. As a result,the central bright fringe shifts to the position where the fifth bright fringe was previously formed. If the thickness of both plates is the same,find the thickness in $\mu m$.

In the figure shown in $YDSE$, a parallel beam of light is incident on the slits from a medium of refractive index $n_1$. The wavelength of light in this medium is $\lambda_1$. $A$ transparent slab of thickness $t$ and refractive index $n_3$ is placed in front of one slit. The medium between the screen and the plane of the slits is $n_2$. The phase difference between the light waves reaching point $O$ (symmetrical, relative to the slits) is: