In a double slit experiment with monochromatic light,fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $5 \times 10^{-2} \,m$ towards the slits,the change in fringe width is $3 \times 10^{-3} \,cm$. If the distance between the slits is $1 \,mm$,then the wavelength of the light will be . . . . . . $nm$.

In the figure, Young's double-slit experiment is shown. $Q$ is the position of the first bright fringe on the right side of $O$. $P$ is the $11^{th}$ fringe on the other side, as measured from $Q$. If the wavelength of the light used is $6000 \times 10^{-10} \text{ m}$, then $S_1B$ will be equal to:

Two light waves of wavelengths $800 \, nm$ and $600 \, nm$ are used in Young's double slit experiment to obtain interference fringes on a screen placed $7 \, m$ away from the plane of the slits. If the two slits are separated by $0.35 \, mm$,then the shortest distance from the central bright maximum to the point where the bright fringes of the two wavelengths coincide will be $............. \, mm$.

The wavelength of light $500 \, nm$ is used in a Young's double slit experiment. The distance between the slits and the screen is $100 \, cm$ and the slits are separated by $1 \, mm$. Find the distance between the fifth $(5^{th})$ and third $(3^{rd})$ bright fringes. (in $mm$)

In a Young's double slit experiment,$16$ fringes are observed in a certain segment of the screen when light of wavelength $700 \,nm$ is used. If the wavelength of light is changed to $400 \,nm$,the number of fringes observed in the same segment of the screen would be........

In Young's double slit experiment shown in the figure,$S_1$ and $S_2$ are coherent sources and $S$ is the screen having a hole at a point $1.0 \, mm$ away from the central line. White light ($400 \, nm$ to $700 \, nm$) is sent through the slits. Which wavelength passing through the hole has strong intensity (in $, nm$)? (Given: $d = 0.5 \, mm$,$D = 50 \, cm$)