$A$ thin transparent plate of thickness $t$ and refractive index $\mu$ is introduced in the path of one of the two interfering waves. The path difference between these waves is changed by half the wavelength of light $\lambda$. The thickness of the plate is

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

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:

$A$ double slit experiment is performed with light of wavelength $500\, nm$. $A$ thin film of thickness $2\, \mu m$ and refractive index $1.5$ is introduced in the path of the upper beam. The location of the central maximum will

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:

$A$ transparent film $(\mu=1.45)$ of thickness $0.02 \ mm$ is placed on one of the slits of a Young's double slit experiment which uses monochromatic light of wavelength $620 \ nm$. How many fringes will cross through the center if the film is removed?