 First minimum of a finite slit array

For $N$ equally spaced, coherently illuminated narrow slits at normal incidence, the phasor sum is proportional to $\sin (N\delta /2)/\sin (\delta /2)$, where $\delta =2\pi d\sin \theta /\lambda$. The first zero around the central maximum has $d\sin \theta =\lambda /N$. Principal maxima are removable zero-over-zero limits, not intensity zeros.