concentration will be maximum for the maximum value of sin β, that is β = π/2. The maximum possible concentration is then In the case that the incident index is not unity, we have and so and in the best-case limit of β = π/2, this becomes If the optic were a collimator instead of a concentrator, the light direction is reversed and conservation of etendue gives us the minimum aperture, S, for a given output full angle 2α. See also Light field Beam parameter product Symplectic geometry Noether's theorem Beam emittance References Further reading Xutao Sun et al., 2006, "Etendue analysis and measurement of light source with elliptical reflector", Displays (27), 56–61. Randall Munroe explains why it's impossible to light a fire with concentrated moonlight using a etendue-conservation argument. Optics