$A$ parallel coherent beam of light falls on a Fresnel biprism of refractive index $\mu$ and refracting angle $\alpha$. The fringe width on a screen at a distance $D$ from the biprism will be (wavelength $= \lambda$).

In a Fresnel's biprism experiment,the distance between the source and the screen is $1 \, m$ and the distance between the source and the biprism is $10 \, cm$. The wavelength of light is $6000 \, \mathring{A}$. The fringe width is $0.03 \, cm$ and the refracting angle of the biprism is $1^\circ$. Find the refractive index of the material of the biprism.

In a biprism experiment,the slit separation is $1 \,mm$. Using monochromatic light of wavelength $5000 \text{ Å}$,an interference pattern is obtained on the screen. Where should the screen be moved,so that the change in fringe width is $12.5 \times 10^{-5} \,m$?

Oil floating on water looks coloured due to interference of light. What should be the order of magnitude of the thickness of the oil layer in order that this effect may be observed? (in $m$)

In a Fresnel's biprism experiment,a mica sheet of refractive index $1.5$ and thickness $6 \times 10^{-6} \ m$ is placed in the path of one of the interfering beams. As a result,the central fringe shifts by a distance equal to $5$ fringe widths. Find the wavelength of light in $\mathring{A}$.

In a biprism experiment, the distance between $4^{th}$ and $13^{th}$ bright band on the same side is '$y$' when light of wavelength $6000 \text{ Å}$ is used. For a light of wavelength '$\lambda$' the distance between $6^{th}$ and $16^{th}$ bright band on the same side is again '$y$'. The value of '$\lambda$' in $\text{Å}$ units is