In Young's double slit experiment,the distance between the slits is $1 \,mm$ and the distance between the slit and the screen is $1 \,m$. If the $10^{th}$ fringe is $5 \,mm$ away from the central bright fringe,then the wavelength of the light used will be.....$\mathring A$.

In Young's double-slit experiment,the intensity at a point on the screen is $I_0/4$. Find the angular position of this point.

In $YDSE$,$16$ fringes occupy a certain region of space with light of wavelength $6000\,\mathring{A}$. If $24$ fringes occupy the same region,the wavelength of the new light is........$\mathring{A}$.

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 a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5 \times 10^{-2} \, m$ towards the slits, the change in fringe width is $3 \times 10^{-5} \, m$. If the separation between the slits is $10^{-3} \, m$, the wavelength of light used is: (in $\text{Å}$)

In a double-slit experiment performed in air, the angular width of a fringe is found to be $0.15^{\circ}$ on a screen placed $80 \ cm$ away. The wavelength of light used is $490 \ nm$. What is the angular width of the fringe if the entire apparatus is immersed in a medium of refractive index $\frac{5}{3}$ (in $^{\circ}$)?