In a $YDSE$,bichromatic light of wavelengths $\lambda_1 = 400\, nm$ and $\lambda_2 = 560\, nm$ is used. The distance between the slits is $d = 0.1\, mm$ and the distance between the plane of the slits and the screen is $D = 1\, m$. The minimum distance between two successive regions of complete darkness is.....$mm$.

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 a certain double-slit experimental arrangement,interference fringes of width $1.0 \ mm$ each are observed when light of wavelength $5000 \ \mathring{A}$ is used. Keeping the setup unaltered,if the source is replaced by another source of wavelength $6000 \ \mathring{A}$,the fringe width will be $...... \ mm$.

In the Young's double slit experiment,the ratio of intensities of bright and dark fringes is $9$. This means that

If yellow light in the Young's double slit experiment is replaced by red light,the fringe width will

$A$ mixture of light,consisting of wavelengths $590 \ nm$ and an unknown wavelength,illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further,it is observed that the $3^{rd}$ bright fringe of the known light coincides with the $4^{th}$ bright fringe of the unknown light. From this data,the wavelength of the unknown light is ...... $nm$.