In an interference pattern,the $(n + 4)^{th}$ blue bright fringe and $n^{th}$ red bright fringe are formed at the same spot. If red and blue light have wavelengths of $7800\,\mathring{A}$ and $5200\,\mathring{A}$ respectively,then the value of $n$ is:

$A$ beam of light consisting of two wavelengths $7000 \; \mathring{A}$ and $5500 \; \mathring{A}$ is used to obtain an interference pattern in Young's double-slit experiment. The distance between the slits is $2.5 \; mm$ and the distance between the plane of the slits and the screen is $150 \; cm$. The least distance from the central fringe,where the bright fringes due to both the wavelengths coincide,is $n \times 10^{-5} \; m$. The value of $n$ is .............

In a double-slit experiment using light of wavelength $600 \; nm$,the angular width of a fringe formed on a distant screen is $0.1^{\circ}$. What is the spacing between the two slits?

In Young's double-slit experiment,the maximum intensity is $I_0$. If one slit is closed,the new maximum intensity is:

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 ......$mm$.

In a Young's double slit experiment,the intensity at a point where the path difference is $\frac{\lambda}{6}$ ($\lambda$ being the wavelength of the light used) is $I$. If $I_0$ denotes the maximum intensity,$I/I_0$ is equal to