= Lagrange optical invariant
{c}
{title2=$H=n(y_1u_2-y_2u_1)$}
For paraxial rays, the <Lagrange optical invariant> is $H=n(y_1u_2-y_2u_1)$. Lossless paraxial ray transfer preserves this quantity: in coordinates $(y,nu)$, free propagation and a <thin lens> act by <matrices> with <determinant> one, which preserve the oriented area of two ray vectors. Consequently a full angular <optical slit> width $\theta$ at an <optical pupil> <diameter> $D$ satisfies $D\theta=A_{\rm cam}p/f_{\rm cam}$ for its image width $p$ and <optical camera> <optical pupil> width $A_{\rm cam}$ in the same meridional plane.
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