In an interference experiment, the third bright fringe is obtained at a point on the screen with light of wavelength $700 \, nm$. What should be the wavelength of the light source in order to obtain the $5^{th}$ bright fringe at the same point (in $nm$)?

$A$ fringe width of a certain interference pattern is $\beta = 0.002 \text{ cm}$. What is the distance of the $5^{\text{th}}$ dark fringe from the center?

Young's double-slit experiment is performed using microwaves of wavelength $\lambda = 3 \, cm$. The distance between the plane of the slits and the screen is $D = 100 \, cm$,and the distance between the slits is $d = 5 \, cm$. Find $(a)$ the number of maxima and $(b)$ their positions on the screen.

Two slits at a distance of $1\, mm$ are illuminated by light of wavelength $6.5 \times 10^{-7}\, m$. The interference fringes are observed on a screen placed at a distance of $1\, m$. The distance between the third dark fringe and the fifth bright fringe will be......$mm$.

Given below are two statements:
Statement $I$: In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits.
Statement $II$: In a Young's double slit experiment, the angular separation of fringes will increase when a monochromatic source is replaced by another monochromatic source of higher wavelength.
In the light of the above statements, choose the correct answer from the options given below:

In Young's double slit experiment,the fringes are displaced by a distance $x$ when a glass plate of refractive index $1.5$ is introduced in the path of one of the beams. When this plate is replaced by another plate of the same thickness,the shift of fringes is $(3/2)x$. The refractive index of the second plate is