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 $............ \ \mathring{A}$.

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.

$A$ ray of light of intensity $I$ is incident on a parallel glass slab at a point $A$ as shown in the figure. It undergoes partial reflection and refraction. At each reflection,$25\%$ of the incident energy is reflected. The rays $AB$ and $A^1B^1$ undergo interference. The ratio $I_{\text{max}} / I_{\text{min}}$ is (in $: 1$)

In a biprism experiment,a steady interference pattern is observed on the screen using light of wavelength $\lambda_1 = 5000 \ Å$. Without disturbing the setup of the experiment,the source of light is replaced by a source of wavelength $\lambda_2 = 6400 \ Å$. The fringe width will:

Which of the following phenomena produces the colour in a soap bubble?

Imperfections in optical lenses can be observed with the help of