The central fringe of the interference pattern produced by light of wavelength $6000 \mathring A$ is found to shift to the position of the $4^{\text {th}}$ bright fringe after a glass plate of refractive index $1.5$ is introduced in front of one slit in Young's experiment. The thickness of the glass plate will be ......... $\mu m$.

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 $d << D, \lambda << d$]

$A$ 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

In a Young's double slit experimental arrangement shown here,if a mica sheet of thickness $t$ and refractive index $\mu$ is placed in front of the slit $S_1$,then the path difference $(S_1P - S_2P)$

In a double slit experiment,when a thin film of thickness $t$ having refractive index $\mu$ is introduced in front of one of the slits,the maximum at the centre of the fringe pattern shifts by one fringe width. The value of $t$ is ($\lambda$ is the wavelength of the light used).

Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $3 \lambda$. The light is collected on a screen $S$ which is placed at a distance $D (>> \lambda)$ from the slits. Find the smallest distance $x$ from the center $O$ such that the point $P$ is a maxima.