= Reversing one slit at an array minimum
{title2=$I_{\rm reversed}=4I_{\rm single}$}
Let a coherent array of identical narrow slits have total far-field <complex amplitude> zero at a chosen direction. Reversing one slit's <phase> by $\pi$ changes its <amplitude> from $a_j$ to $-a_j$, so the new total is $-2a_j$. Its <intensity> is four times the single-slit <intensity>, independent of which slit was changed. For $N$ equally spaced slits, adjacent <phase> step $2\pi m/N$ gives such a zero when $m$ is not a multiple of $N$. A finite slit envelope multiplies the common <intensity> factor.
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