Is there a negative numerical aperture(NA)?

Question

[Collimated beam - Negative lens] Can this situation call negative NA?

or Is there a exist any negative NA situation?

Thanks

Answer 1

No, there's really not such a thing as a negative numerical aperture. Understand that NA is about an image forming lens, bringing the incoming light (in the case you mentioned, collimated) to a single focus point. Meaning, a net-convex system.

I understand that it's tempting to look at an equation such as NA = n sin θ, and wonder what meaning can be inferred if n or θ were negative.

• In the case of negative index of refraction (negative n), it doesn't change NA. The classical formulation of numerical aperture didn't anticipate metamaterials with negative refractive indices. In that case, the equation should probably be updated to NA = |n| sin θ.
• negative θ is nonsensical. The acceptance angle is a measurement of a real-world value, where in this case negative angle doesn't exist in reality.