In a biprism experiment,the $6^{\text{th}}$ bright band with wavelength $\lambda_1$ coincides with the $7^{\text{th}}$ dark band with wavelength $\lambda_2$. Then the ratio $\lambda_1 : \lambda_2$ is (other settings remain the same):

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.

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 $\mathring{A}$?

Light of wavelength $6000 \text{ Å}$ is incident on a thin glass plate of refractive index $\mu = 1.5$ such that the angle of refraction into the plate is $60^{\circ}$. Calculate the smallest thickness of the plate which will make a dark fringe by reflected beam interference.

If Fresnel's biprism experiment is performed in water instead of air,what will be the effect on the fringe width?

The thickness of a plate having refractive index $\mu$ which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it is