Numeric Aperture & Working Distance?

[Oldbear67]

Beginner question:
What is the (not too mathematical) relationship between numeric aperture and working distance?

I get that smaller NA means longer working distances, but when I look at some lenses it isn't clear.

[Scarodactyl]

It's complicated by the relationship with the lens diameter as well, but you can get a sort of intuitive sense of it by looking at the definition of numerical aperture in relation to the light cone that the lens can capture.

[rjlittlefield]

Smaller NA does not necessarily mean larger working distance. There are some highly corrected objectives with low magnification and small NA whose working distances are quite short.

However, large NA always means either short working distance or large diameter, in order that the lens can accept the wide range of angles corresponding to large NA.

--Rik