Perfect converging lens. Object is imaged by refraction to a real image distant from the focal point in Image Space.
Resolution: Smallest "measurable" size; or smallest "resolvable feature size" in a microscope optical system.

Abbe based his definition of resolution only on the objective Numerical Aperture (NA) and wavelength.

For telescopes and general lenses:
Rayleigh resolution for BF:
A point object will be imaged as a series of concentric rings due to wave interaction (constructive and destructive interference). The central maximum (diameter = d) is termed the Airy disc.
Two closely spaced objects may be resolved only if their Airy discs are sufficiently far apart. As the objects are placed closer together (A–C), the resulting diffraction patterns (Airy discs) merge into one, non-resolvable, central pattern (D).

The Rayleigh criterion, defined as the minimum resolvable detail, when the first diffraction minimum of the image of one source point coincides with the maximum of another (C).

d=smallest resolvable feature; lambda=wavelength of light; n=the refractive index of the medium between the sample and lens; theta=the half Angular Aperture.
Recall that NA=nsin(Angular Aperture/2)
d=min distance; f=focal length of the lens; l = wavelength of light, D=diameter of the (telescope) lens.
Magnification of a simple magnifier is defined several ways:


Here is a good reference for Visual Magnification

Abbe resolution:
Therefore:
For fluorescence microscopy:
Rayleigh based his definition of resolution on the diffraction of light and overlapping diffraction patterns, as well as wavelength, and NA, by the imaging lens system. It is defined as the minimum distance separating two adjacent Airy discs allowing them to be distinguished as separate. The constant "1.22" accounts for overlapping Airy diffraction patterns.
As a convention, in resolution equations we use the half Angular Aperture: