The colours observed in thin soap bubbles are due to

$A$ 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.]

$A$ plano-convex lens is placed with its curved surface on a plane glass plate,creating a thin air film. With monochromatic light,this thin film produces an interference pattern due to reflections from the top curved surface and the bottom glass plate surface.
Statement-$1$: When light is reflected from the air-glass plate interface,it undergoes a phase change of $\pi$.
Statement-$2$: The center of the interference pattern is dark.

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.

$A$ thin oil film of refractive index $1.2$ floats on the surface of water $(\mu = \frac{4}{3})$. When light of wavelength $\lambda = 9.6 \times 10^{-7} \ m$ falls normally on the film from air,it appears dark when seen normally. What is the minimum change in its thickness for which it will appear bright in normally reflected light by the same light?

$A$ Fresnel's biprism experiment is performed in water. If the fringe width in air is $\beta_a$,and the refractive indices of the biprism material and water are $1.5$ and $1.33$ respectively,find the new fringe width.