Two coherent monochromatic point sources $S_{1}and{S}_2$ of wavelength $\lambda =600nm$ are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance d=1.8mm. 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 $\Delta \theta$. Which of the following options is/are correct?

$d=1.8\times {10}^{-3}m=18\times {10}^{-4}m and \lambda =6\times {10}^{-7}m$

Path difference at point P (as shown)
  $\Delta x=S_{1}P-S_{2}P=d\sin \theta ,$
where $\theta$  angle is measured from vertical line as shown.
For bright fringe,  $d\sin \theta =m\lambda \mathrm{...}\left(\text{i}\right)$
Point $P_1$ is the point difference  $\left(\Delta x\right)=d$  
If  $P_2$ is the point of bright fringe, then
$d=m\lambda \Rightarrow m=\frac{d}{\lambda }=300$       
$\therefore$ Total number of fringes = 3000
At  $P_2$, the order of fringe will be maximum.
$\therefore$  Options (C) and (D) are correct.
On differentiating Eq. (i)
$d\cos \theta \left(\Delta \theta \right)=\left(\Delta m\right)\lambda =$  constant for consecutive bright fringe.
If  $\cos \theta$ decreases,  $\Delta \theta$ increases as  $\theta$ varies from 0 to  $\frac{\pi }{2}$
 $\therefore$ Option (B) is incorrect.