In a biprism experiment,the $4^{\text{th}}$ dark band is formed opposite to one of the slits. The wavelength of light used is ($D=$ distance between source and screen,$d=$ distance between the slits).

In a biprism experiment, the maximum intensity is $I_0$. If the path difference between the two interfering waves is $\frac{\lambda}{3}$, then the intensity at the point on the screen is [$\sin 30^{\circ} = \cos 60^{\circ} = 0.5, \sin 60^{\circ} = \cos 30^{\circ} = \sqrt{3}/2$].

In a Fresnel's biprism experiment,the fringe width is $1 \,mm$. The distance of the nearest dark fringe from the central bright fringe is .......$mm$.

$A$ biprism experiment is set up as shown. When the upper half area of the biprism is covered with an opaque material,then:

Light of wavelength $6000 \, \mathring{A}$ is incident on a thin glass plate of refractive index $1.5$ such that the angle of refraction in the plate is $60^\circ$. Find the thickness of the plate so that it appears dark in reflection.

White light may be considered to be a mixture of waves with $\lambda$ ranging between $3900\ \mathring A$ and $7800\ \mathring A$. An oil film of thickness $10,000\ \mathring A$ is examined normally by reflected light. If $\mu = 1.4$,then the film appears bright for