$A$ 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 biprism experiment,monochromatic light of wavelength $\lambda$ is used. The distance between two coherent sources $d$ is kept constant. If the distance between the slit and the eyepiece $D$ is varied as $D_1, D_2, D_3$ and $D_4$,and the corresponding measured fringe widths are $Z_1, Z_2, Z_3$ and $Z_4$,then:

The following diagram is an arrangement to view the interference pattern produced by a wedge of liquid between a microscope slide and a glass block. The interference pattern obtained is made of equally spaced parallel fringes. The fringe separation (or fringe width) $\beta$ may be decreased by some of the following actions (Consider one change at a time).

$A$ Fresnel's biprism experiment is performed in water. If the fringe width in air is $\beta_a$,and the refractive indices of the biprism material and water are $1.5$ and $1.33$ respectively,find the new fringe width.

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

The approximate thickness of an oil film required to observe the interference of light (due to which it appears coloured) is .......