In an interference arrangement similar to Young's double-slit experiment, the slits $S_1$ and $S_2$ are illuminated with coherent microwave sources, each of frequency ${10}^6 \mathrm{Hz}.$ The sources are synchronized to have zero phase difference. The slits are separated by a distance$d=150.0 \mathrm{m}$ and the screen is at a very large distance from slits. The intensity $I\mathit{ }\left(\mathrm{\theta }\right)$ is measured as a function of $\mathrm{\theta }$, where $\mathrm{\theta }$ is defined as shown. Screen is at a large distance. If $I_0$ is the maximum intensity then $I \left(\mathrm{\theta }\right)$ for $0 \le \mathrm{\theta }\le 90º$ is given by:

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?