In $YDSE$, a thin film $(\mu=1.6)$ of thickness $0.01 \,mm$ is introduced in the path of one of the two interfering beams. The central fringe moves to a position occupied by the $10^{\text{th}}$ bright fringe earlier. The wavelength of the wave is ......... $\mathring{A}$.

In the figure shown,if a parallel beam of white light is incident on the plane of the slits,then the distance of the white spot on the screen from $O$ is [Assume $d << D, \lambda << d$].

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 ..................... $\mu m$.

$6300 \mathring A$ 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:

In Young's double-slit experiment,a glass plate of refractive index $1.5$ and thickness $5 \times 10^{-4} \,cm$ is kept in the path of one of the light rays. Then

In a Young's double-slit experiment,light of wavelength $4800 \, \mathring A$ is used. If both slits are covered by transparent plates of the same thickness $t$ having refractive indices $\mu_1 = 1.5$ and $\mu_2 = 1.8$,and the central bright fringe shifts to the position of the fifth bright fringe,then the thickness of the plates is ....... $\mu m$.