In a double-slit experiment,green light $(5303\,\mathring{A})$ falls on a double slit having a separation of $19.44\,\mu m$ and a width of $4.05\,\mu m$. The number of bright fringes between the first and the second diffraction minima is

Calculate the wavelength of light used in an interference experiment from the following data: Fringe width $\beta = 0.03 \, cm$. The distance between the slits and the eyepiece is $D = 1 \, m$. The distance between the images of the virtual source,when a convex lens of focal length $f = 16 \, cm$ is used at a distance of $v = 80 \, cm$ from the eyepiece,is $d' = 0.8 \, cm$.

Young's double slit experiment is performed with monochromatic light. $A$ thin film is introduced in front of one of the slits.

In Young's double slit experiment, two slits $S_1$ and $S_2$ are $d$ distance apart and the separation from slits to screen is $D$ (as shown in figure). Now, if two transparent slabs of equal thickness $0.1 \, mm$ but refractive indices $1.51$ and $1.55$ are introduced in the path of the beam $(\lambda = 4000 \, \mathring{A})$ from $S_1$ and $S_2$ respectively, the central bright fringe spot will shift by $..........$ number of fringes.

In a Young's double slit experiment,each of the two slits $A$ and $B$,as shown in the figure,are oscillating about their fixed center with a mean separation of $0.8 \ mm$. The distance between the slits at time $t$ is given by $d = (0.8 + 0.04 \sin \omega t) \ mm$,where $\omega = 0.08 \ rad \ s^{-1}$. The distance of the screen from the slits is $1 \ m$ and the wavelength of the light used to illuminate the slits is $6000 \ \mathring A$. The interference pattern on the screen changes with time,while the central bright fringe (zeroth fringe) remains fixed at point $O$.
$(1)$ The $8^{\text{th}}$ bright fringe above the point $O$ oscillates with time between two extreme positions. The separation between these two extreme positions,in micrometer $(\mu m)$,is. . . . .
$(2)$ The maximum speed in $\mu m/s$ at which the $8^{\text{th}}$ bright fringe will move is. . . . .

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).