The distance of the $5^{\text{th}}$ dark fringe from the center is $4 \, mm$. If $D = 2 \, m$ and $\lambda = 600 \, nm$,then the distance between the slits is (in $mm$):

In Young's double slit experiment,the intensity at a point is $1/4$ of the maximum intensity. The angular position of this point is:

In $Y.D.S.E.$,the separation between the two slits $S_1$ and $S_2$ is $a$,and the screen is at a distance $x$ from the slits. The light source $S$ is moving with velocity $v$ parallel to the line joining $S_1$ and $S_2$ and is at a perpendicular distance $h$ from the plane of the slits. What is the frequency of change in brightness at the central point on the screen?

In two different Young's double-slit experiments,the fringe width is the same when the ratio of wavelengths is $1:2$. If the ratio of the distance between the slits in the two cases is $2:1$,then the ratio of the distance between the slits and the screen in the two experiments is:

In the Young's double slit experiment with sodium light,the slits are $0.589 \ m$ apart. The angular separation of the third maximum from the central maximum will be (given $\lambda = 589 \ nm$):

In a Young's Double slit experiment,the first maxima is observed at a fixed point $P$ on the screen. Now,the screen is continuously moved away from the plane of the slits. The ratio of the intensity at point $P$ to the intensity at point $O$ (centre of the screen) is: