= Optical momentum of a ray
{title2=$p=\mu t,\quad dp/ds=\nabla\mu$}
For a <light ray> parametrized by <arc length> $s$, with <unit tangent vector> $t$ in a smooth positive <refractive index> $\mu$, the optical momentum is $p=\mu t$. This is the momentum for optical path-length normalization. The <Euler-Lagrange equation> for <Fermat principle>, $\int\mu(r)|r'(\tau)|d\tau$, gives $d(\mu t)/ds=\nabla\mu$. Therefore an index independent of $z$ conserves $p_z=\mu\,dz/ds$. In coordinates $r(z),\theta(z)$ this is $\mu/\sqrt{1+r'^2+r^2\theta'^2}$, the first integral supplied by the <Beltrami identity for several dependent variables>.
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