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. The wavelength of light used is .... $\mathring{A}$

Assertion: Thin films such as a soap bubble or a thin layer of oil on water show beautiful colours when illuminated by white light.
Reason: It happens due to the interference of light reflected from the upper surface of the thin film.

$A$ thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be

In two separate setups for a Biprism experiment using the same wavelength,fringes of equal width are obtained. If the ratio of slit separation is $2:3$,then the ratio of the distance between the slit and the screen in the two setups is:

In a biprism experiment using sodium light $\lambda_1 = 6000\, \mathring{A}$,an interference pattern is obtained in which $20$ fringes occupy $2\, cm$. On replacing sodium light by another source of wavelength $\lambda_2$ without making any other change,$30$ fringes occupy $2.7\, cm$ on the screen. What is the value of $\lambda_2$ 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