= First subsidiary maximum of a large slit array
{title2=$I_{\rm main}/I_{\rm sub}\simeq9\pi^2/4$}
For $N$ equal narrow slits, adjacent <phase> increment $\delta$ gives <amplitude> $\sin(N\delta/2)/\sin(\delta/2)$ relative to one slit. Near a principal maximum, set $u=N\delta/2$; for large $N$ the normalized <intensity> approaches $(\sin u/u)^2$. Approximating the first subsidiary maximum by $u=3\pi/2$ gives principal-to-subsidiary <intensity> ratio $9\pi^2/4$. The exact large-array extremum satisfies $\tan u=u$ in $(\pi,2\pi)$ and gives a slightly different ratio, about $21.2$. The slit envelope can further modify observed peak heights.
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