In a $YDSE$ apparatus,two identical slits are separated by $1\, mm$ and the distance between the slits and the screen is $1\, m$. The wavelength of light used is $6000\, \mathring{A}$. The minimum distance between two points on the screen having $75\%$ intensity of the maximum intensity is ......$mm$.

$A$ beam of light consisting of two wavelengths $6300 \, \mathring{A}$ and $\lambda \, \mathring{A}$ is used to obtain interference fringes in a Young's double-slit experiment. If the $4^{th}$ bright fringe of $6300 \, \mathring{A}$ coincides with the $5^{th}$ dark fringe of $\lambda \, \mathring{A}$,the value of $\lambda$ (in $\mathring{A}$) is:

$A$ double slit experiment is immersed in water of refractive index $1.33$. The slit separation is $1 \,mm$, and the distance between the slit and the screen is $1.33 \,m$. The slits are illuminated by light of wavelength $6300 \,Å$. The fringe width is:

In Young's double slit experiment,the slits are $0.5 \, mm$ apart and the interference is observed on a screen at a distance of $100 \, cm$ from the slits. It is found that the $9^{th}$ bright fringe is at a distance of $7.5 \, mm$ from the $2^{nd}$ dark fringe on the same side of the central fringe. The wavelength of the light used is ..... $\mathring{A}$.

In Young's double slit experiment,the distance between the slits is reduced to half and the distance between the slit and the screen is doubled,then the fringe width:

$A$ source simultaneously emitting light at two wavelengths $400 \,nm$ and $800 \,nm$ is used in the Young's double slit experiment. If the intensity of light at the slit for each wavelength is $I_{0}$,then the maximum intensity that can be observed at any point on the screen is