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 $7^{th}$ bright fringe. Find the wavelength of the light used.

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.

This question has a paragraph followed by two statements,Statement $- 1$ and Statement $- 2$. Of the given four alternatives after the statements,choose the one that describes the statements.
$A$ thin air film is formed by putting the convex surface of a plano-convex lens over a plane glass plate. With monochromatic light,this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.
Statement $- 1$: When light reflects from the air-glass plate interface,the reflected wave suffers a phase change of $\pi$.
Statement $- 2$: The centre of the interference pattern is dark.

Oil floating on water looks coloured due to interference of light. What should be the order of magnitude of the thickness of the oil layer in order that this effect may be observed? (in $m$)

Assertion: Newton's rings are formed in the reflected system when the space between the lens and the glass plate is filled with a liquid of refractive index greater than that of glass; the central spot of the pattern is bright.
Reason: This is because the reflection in these cases will be from a denser to rarer medium and the two interfering rays are reflected under similar conditions.

$A$ light of wavelength $5890 \; \mathring{A}$ falls normally on a thin air film. What is the minimum thickness of the film such that the film appears dark in reflected light?