Resolution
Numerical aperture (NA) can be used to calculate the resolution (r). Resolution is the smallest object that the lens can resolve.
Higher NA resolves more detail. This is a butterfly scale with NA 0.5 and NA 0.8.
M Plan ELWD 40x NA 0.5 and M Plan Apo 40x NA 0.8.
200x on sensor, viewed at 200%. The red arrows show the stripe/ridge that I tried to have in focus. At this resolution it is possible to resolve structures between the stripes/ridges.
Resolution: r = λ / (2 * NA)
Butterfly scales can be a good target for testing lenses and their resolution. This is Peacock butterfly scales, NA 0.6. At this NA it is easy to observe stripes/ridges on the scales. From NA 0.3 it is usually possible to see the stripes/edges.
Example calculations of resolution using the simple formula for resolution (r) in air using the wavelength (λ) for green light 0.550 µm (micro meter).
Case #1: NA=0.14 for example Mitutoyo M plan 5x
r = 0.550µm / (2 * 0,14) ≈ 2µm
Case #2: NA=0.3 for example Nikon TU plan 10x
r = 0.550µm / (2 * 0,3) ≈ 1µm
Note: Camera sensor pixel size
On a camera sensor roughly 3 pixels are needed to resolve something. So for a 5x NA 0.15 that resolves a subject of size 2µm the smallest camera sensor pixel size needed is 6,7µm (2µm*5x/3) to resolve the details. For a 10x NA 0.3 the smallest pixel size is the same 6,7µm (1 µm*10x/3).