While conducting the Young's double-slit experiment, a student replaced two slits with a large opaque plate in the $x-y$ plane containing two small holes that act as two coherent point sources $(S_1, S_2)$ emitting light of wavelength $600 \mathrm{nm}.$ The student mistakenly placed the screen parallel to the $x-z$ plane $(z> 0)$ at a distance$D= 3 \mathrm{m}$ from the mid-point of$S_1{S}_2,$as shown schematically in the figure. The distance between the sources $d=0.6003 \mathrm{mm}$. The origin $O$ is at the intersection of the screen and the line joining $S_1{S}_2.$ Which of the following is(are) true of the intensity pattern on the screen?

Two coherent monochromatic point sources $S_1$ and $S_2$ of wavelength $\mathrm{\lambda }= 600 \mathrm{nm}$are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance $d= 1.8 \mathrm{mm}.$ This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $∆\mathrm{\theta }.$ Which of the following options is/are correct? 

Direction: The 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 plane-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.

$\mathrm{Statement}-1:$ When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\mathrm{\pi }$.

$\mathrm{Statement}-2:$ The centre of the interference pattern is dark. 

Two coherent point sources$\mathit{ }{S}_1$ and $S_2$ are separated by a small distance $\text{'}d\text{'}$ as shown. The fringes obtained on the screen will be: