Two point sources separated by 2.0 m are radiating in phase with $\lambda =0.50m$. A detector moves in a circular path around the two sources in a plane containing them. How many maxima are detected?

Condition for maxima is

$$\begin{gathered} d\sin \theta =n\lambda \\ \sin \theta =\frac{n\lambda }{d}=n\left(\frac{0.50}{2.0}\right)=0.25m \end{gathered}$$

As  $\sin \theta$ lies between -1  and 1, so we wish to find all values of n for which
$\left|0.25n\right|\le 1$
These values are  $-4,-3,-2,-1,0,+1,+2,+3,+4$ For each of these, there are two different values of $\theta$ except for $-4$  and $+4$. A single value of  $\theta , -{90}^0$ and  $+{90}^0$ is associated with  $n=-4$ and  $n=+4$   respectively. Thus, there are 16 different angles in all and therefore 16 maxima.