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 $YDSE$, 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 ......... $\mathring{A}$.

Interference fringes were produced in Young's double slit experiment using light of wavelength $5000 \, Å$. When a film of material $2.5 \times 10^{-3} \, cm$ thick was placed over one of the slits, the fringe pattern shifted by a distance equal to $20$ fringe widths. The refractive index of the material of the film is

$6300 \mathring A$ 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:

When a glass plate of refractive index $1.44$ is introduced in the path of one of the interfering beams, the fringes are displaced by a distance '$y$'. If this plate is replaced by another plate of same thickness but of refractive index $1.66$, the fringes will be displaced by a distance

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 . . . . . . .