In an ideal Young's double-slit experiment,a glass plate of thickness $t$ and refractive index $\mu = 1.5$ is placed in the path of one of the interfering beams. If the central bright fringe shifts to the position originally occupied by the first bright fringe (corresponding to wavelength $\lambda$),then the minimum thickness $t$ of the glass 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

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:

$A$ plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double slit experiment. What should be the minimum thickness $t$ for which the intensity at the centre of the fringe pattern is zero?

Young's double slit experiment is conducted in a liquid of refractive index $\mu_1$ as shown in the figure. $A$ thin transparent slab of refractive index $\mu_2$ and thickness $t$ is placed in front of the slit $S_2$. The magnitude of the optical path difference at point $O$ is

Consider the figure (not drawn to scale) in which a converging lens of radius $R = 1 \ cm$ and focal length $f = 20 \ cm$ is cut in the middle. The upper part is lifted up by $d = 1 \ mm$ and the lower part is pulled down by the same distance. The gap between them is blocked by an opaque sheet. $A$ point light source with wavelength $\lambda = 500 \ nm$ is placed on the optical axis at a distance of $2f$ from the split lens. $A$ large screen is placed at $L = 1 \ m$ from the right focus of the lens. Find the approximate number of interference fringes on the screen.