$A$ soap film with refractive index $\mu = 4/3$ is illuminated by white light incident at an angle of $60^\circ$. $A$ dark band corresponding to a wavelength of $5500 \, \mathring{A}$ is observed in the reflected light. Find the minimum thickness of the film in $\mathring{A}$.

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 of the second dark fringe from the central fringe is $3 \ mm$. The distance of the sixth bright fringe from the central fringe is (in $mm$)

In a Fresnel's biprism experiment,fringes are obtained in the focal plane of an eyepiece at a distance of $1 \ m$ from the slit. $A$ convex lens is placed between the biprism and the eyepiece. The images of the slit are formed at two positions of the lens. The distances between the two images of the slit at these two positions are $4.05 \times 10^{-3} \ m$ and $2.9 \times 10^{-3} \ m$ respectively. Calculate the distance between the slits.

Light is incident on a glass plate $(\mu = 1.5)$ such that the angle of refraction is $60^\circ$. $A$ dark band is observed corresponding to a wavelength of $6000 \, \mathring A$. If the thickness of the glass plate is $1.2 \times 10^{-3} \, mm$,find the order of the interference band.

In a biprism experiment, the distance of the source from the biprism is $1 \, m$ and the distance of the screen from the biprism is $4 \, m$. The refracting angle of the biprism is $\alpha = 2 \times 10^{-3} \, \text{radians}$. The refractive index $\mu$ of the biprism is $1.5$ and the wavelength of light used is $\lambda = 6000 \, \mathring{A}$. How many fringes will be seen on the screen?