The NA (numerical aperture) of the lens is an index for judging the brightness, resolution and depth of focus of the lens.
NA = n × sin θ.
From above picture, 0 <θ <90 °.
It means 0 <NA <1. (In air)
(NA is determined by θ and refractive index.)
NA is larger, the lens will be brighter.
Light always tries to spread. (Diffraction)
It is necessary to narrow down at the largest possible angle in order to narrow down
NA is larger, the resolution is higher too. (When comparing at the same magnification)
The resolution = (0.61 × λ) / NA.
NA is higher, the depth of focus becomes shallower
The depth of focus = λ / (the square of NA).
Most of the microscope objective lenses have NA information.
C mount zoom lens will change significantly depend on magnification.
(The lens principal point (theoretical value) will change by changing the lens magnification.)
The following is an excerpt from a catalog of a manufacturer.
With a very special C mount zoom lens, NA does not fluctuate as shown below.
However, it becomes larger and more expensive.