$A$ transparent film of refractive index $2.0$ is coated on a glass slab of refractive index $1.45$. What is the minimum thickness of the transparent film to be coated for the maximum transmission of green light of wavelength $550 \ \text{nm}$ (in $\text{nm}$)? [Assume that the light is incident nearly perpendicular to the glass surface.]

$A$ 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 $\mathring{A}$.

To ensure almost $100$ per cent transmittivity,photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediate between that of air and glass (which makes the optical element of the lens). $A$ typically used dielectric film is $MgF_2$ $(n = 1.38)$. What should the thickness of the film be so that at the center of the visible spectrum $5500 \, \mathring{A}$ there is maximum transmission?

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 .......$mm$.

White light is incident at an angle of $30^\circ$ on a soap film with a refractive index of $4/3$. The wavelength of the transmitted light is observed to be $6 \times 10^{-5} \, cm$. Find the minimum thickness of the film.

The colors seen on an oil film floating on the surface of water are due to interference. What should be the order of the thickness of the oil film?