In a Young's double-slit experiment,the slits are separated by $0.12 \, mm$ and the screen is at a distance of $1 \, m$. Find the distance of the $3^{rd}$ dark fringe from the center of the screen in $cm$. Given $\lambda = 6000 \, \mathring{A}$.

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 Young's double-slit experiment,we get $10$ fringes in the field of view using monochromatic light of wavelength $4000 \text{ } \mathring{A}$. If we use monochromatic light of wavelength $5000 \text{ } \mathring{A}$,then the number of fringes obtained in the same field of view is

In Young's double-slit experiment,monochromatic light is used to illuminate the two slits $A$ and $B$. Interference fringes are observed on a screen placed in front of the slits. If a thin glass plate is placed normally in the path of the beam coming from slit $A$,then:

Minimum thickness of a mica sheet having $\mu = 3/2$ which should be placed in front of one of the slits in $YDSE$ is required to reduce the intensity at the centre of the screen to half of the maximum intensity is-

The fringe width in Young's double-slit experiment increases when: