The central fringe of an interference pattern produced by light of wavelength $6000 \, \mathring{A}$ is found to shift to the position of the fourth bright fringe after a glass plate of refractive index $1.5$ is introduced in front of one slit. The thickness of the glass plate would be ...... $\mu m$.

The slits in a double-slit interference experiment are illuminated by orange light $(\lambda = 600 \ nm)$. $A$ thin transparent plastic sheet of thickness $t$ is placed in front of one of the slits. The number of fringes $(N)$ shifting on the screen is plotted versus the refractive index $\mu$ of the plastic in the graph shown. The value of $t$ is

Light of wavelength $500 \, nm$ is used to form an interference pattern in Young's double-slit experiment. $A$ uniform glass plate of refractive index $1.5$ and thickness $0.1 \, mm$ is introduced in the path of one of the interfering beams. The number of fringes by which the central maximum shifts is

As shown in the figure,in Young's double slit experiment,a thin plate of thickness $t = 10\,\mu m$ and refractive index $\mu_1 = 1.2$ is inserted in front of slit $S_1$. The experiment is conducted in air $(\mu = 1)$ and uses a monochromatic light of wavelength $\lambda = 500\,nm$. Due to the insertion of the plate,the central maxima is shifted by a distance of $x\beta_0$,where $\beta_0$ is the fringe-width before the insertion of the plate. The value of $x$ 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 $d' = 0.8 \, cm$.

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. . . . .