When a mica sheet of thickness $7 \ \mu m$ and refractive index $\mu = 1.6$ is placed in the path of one of the interfering beams in a biprism experiment, the central fringe shifts to the position of the seventh bright fringe. The wavelength of the light used is $............ \ \mathring{A}$.

$A$ thin transparent film with refractive index $1.4$ is held on a circular ring of radius $1.8 \ cm$. The fluid in the film evaporates such that transmission through the film at wavelength $560 \ nm$ goes to a minimum every $12 \ seconds$. Assuming that the film is flat on its two sides, the rate of evaporation is . . . . . . $\pi \times 10^{-13} \ m^3/s$.

In a biprism experiment,$21$ fringes are observed in a given region using light of wavelength $4800 \text{ Å}$. If light of wavelength $5600 \text{ Å}$ is used,the number of fringes in the same region will be:

Assertion: At the first glance,the top surface of the Morpho butterfly's wing appears a beautiful blue-green. If the wind moves the colour changes.
Reason: Different pigments in the wing reflect light at different angles.

$A$ 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.

In a biprism experiment,monochromatic light of wavelength $\lambda$ is used. The distance between two coherent sources is kept constant. If the distance between the slit and the eyepiece $(D)$ is varied as $D_{1}, D_{2}, D_{3}$ and $D_{4}$,and the corresponding measured fringe widths are $z_{1}, z_{2}, z_{3}$ and $z_{4}$,then: