Question
While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the $x-y$ plane containing two small holes that act as two coherent point sources $\left(S_1, S_2\right)$ emitting light of wavelength $600 \mathrm{~nm}$. The student mistakenly placed the screen parallel to the $x-z$ plane (for $z>0$ ) 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 $\mathrm{O}$ 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?
($A$) Straight bright and dark bands parallel to the $x$-axis
($B$) The region very close to the point $O$ will be dark
($C$) Hyperbolic bright and dark bands with foci symmetrically placed about $\mathrm{O}$ in the $x$-direction
($D$) Semi circular bright and dark bands centered at point $\mathrm{O}$