$A$ thin mica sheet of thickness $2 \times 10^{-6} \ m$ and refractive index $\mu = 1.5$ is introduced in the path of the first wave. The wavelength of the wave used is $5000 \ \mathring{A}$. The central bright maximum will shift:

$6300 \mathring A$ wavelength light shines on two narrow slits separated by a distance of $1.0 \ mm$ and illuminates a screen at a distance of $1.5 \ m$ away. When one slit is covered by a thin glass plate of refractive index $1.8$ and the other slit by a thin glass plate of refractive index $\mu$,the central maxima shifts by $6^o$. Both plates have the same thickness of $0.5 \ mm$. The value of the refractive index $\mu$ of the plate is:

$A$ flake of glass (refractive index $\mu = 1.5$) is placed over one of the openings of a double slit apparatus. The interference pattern displaces itself through seven successive maxima towards the side where the flake is placed. If the wavelength of the light used is $\lambda = 600 \, nm$,then the thickness of the flake is ........ $nm$.

If a thin mica sheet of thickness $t$ and refractive index $\mu = 5/3$ is placed in the path of one of the interfering beams as shown in the figure,then the displacement of the fringe system is:

In a double-slit experiment,the wavelength $\lambda$ of the light source is $400 \ nm$,the slit separation $d$ is $20 \ \mu m$,and the individual slit width $a$ is $4 \ \mu m$. Considering the interference of light from the two slits and the diffraction of light through each slit,find the number of bright interference fringes that lie within the central peak of the diffraction envelope.

In the $YDSE$ shown,the two slits are covered with thin sheets having thickness $t$ and $2t$,and refractive index $2\mu$ and $\mu$ respectively. Find the position $(y)$ of the central maxima.