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........

Two slits are separated by $0.3\, mm$. $A$ beam of $500\, nm$ light strikes the slits producing an interference pattern. Find the number of maxima observed in the angular range $-30^{\circ} < \theta < 30^{\circ}$.

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

In Young's double-slit experiment,a thin mica sheet of thickness $12 \times 10^{-7} \ m$ is placed in the path of one of the interfering beams. It is observed that the central bright fringe shifts by a distance equal to the fringe width. If the wavelength of light used is $6 \times 10^{-7} \ m$,find the refractive index of the mica sheet.

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 Young's double slit experiment, two slits are illuminated with light of wavelength $\lambda$. The line joining $A_1P$ is perpendicular to $A_1A_2$. If the first minimum is detected at $P$, the value of slit separation '$a$' will be (where $D$ is the distance between the source and the screen):