$A$ double-slit experiment is performed with light of wavelength $500 \ nm$. If a thin plate of thickness $2 \ \mu m$ and refractive index $1.5$ is placed in front of one of the slits,the central fringe will shift by:

In a Young's double-slit experiment,light of wavelength $4800 \, \mathring{A}$ is used. One slit is covered by a thin transparent plate of refractive index $1.4$ and the other slit is covered by another thin transparent plate of refractive index $1.7$. As a result,the central bright fringe shifts to the position where the fifth bright fringe was previously formed. If the thickness of both plates is the same,find the thickness in $\mu m$.

In a Young's double slit experiment with light of wavelength $\lambda ,$ the fringe pattern on the screen has a fringe width $\beta .$ When two thin transparent glass (refractive index $\mu$) plates of thickness $t_1$ and $t_2$ $(t_1 > t_2)$ are placed in the path of the two beams respectively,the fringe pattern will shift by a distance:

$A$ transparent medium of refractive index $\mu = 1.5$ and thickness $t = 2.5 \times 10^{-5} \, m$ is placed in front of one of the slits in a Young's double-slit experiment. By what distance (in $cm$) will the interference pattern shift? The distance between the two slits is $d = 0.5 \, mm$ and the distance between the screen and the slits is $D = 100 \, cm$.

In the ideal double-slit experiment,when a glass plate (refractive index $\mu = 1.5$) of thickness $t$ is introduced in the path of one of the interfering beams (wavelength $\lambda$),the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is:

In the figure shown,if a parallel beam of light is incident on the plane of the slits at an angle such that the path difference at point $O$ is $\Delta x = d \sin \theta = d \cdot (\frac{2d/3}{d}) = \frac{2d}{3}$,and if point $O$ is a maxima for monochromatic light,then which of the following cannot be the wavelength of the incident light? [Assume $d << D, \lambda << d$]