= Exact half-period zone radii
{title2=$r_n^2=nf\lambda+n^2\lambda^2/4$}
For a <plane wave> incident on a flat <zone plate>, the path difference from <radius> $r_n$ to axial focal distance $f$ is $\sqrt{f^2+r_n^2}-f$. Setting it equal to $n\lambda/2$ gives the title relation. The paraxial limit is $r_n\simeq\sqrt{nf\lambda}$, and the fine outer-zone width is approximately $f\lambda/(2r_n)$. Alternately removing half-period annuli makes the remaining contributions reinforce at the principal focus. Choosing the number of zones sets the aperture and fabrication scale, not the principal focal distance independently of these <radii>.
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