The resolving power of an instrument is a measure of how well it can distinguish between two (apparently) very close sources of light. To illustrate this we will consider an astronomical telescope.
Even when using a telescope of high magnification, the image of a star should be a very small point of light. This is because even the closest stars ware very far away. In practice, the image is not a point because the light from the star is diffracted as it enters the telescope. The effect is exaggerated in the following diagrams.

If two stars are far from each other, it is still obvious that they are two separate light sources.

However, if they are (apparently) close together, the diffraction causes their images to overlap.
Rayleigh suggested that the images should be considered as just resolved if the central maximum of one image coincides with the first minimum of the other image, as shown in the next diagram.

This idea is now called the Rayleigh criterion and (for a circular aperture)… it can be shown that it corresponds to the light sources having an angular separation* , given by

= the wavelength of the light
b = the diameter of the object lens of the telescope
*The two stars in the diagram below have an angular separation of q from the point of view of the observer. Notice that they are not, in fact, very close to each other.

Exmples of resolving Power
A standard benchmark for the resolvance of a grating or other spectroscopic instrument is the resolution of the sodium doublet. The two sodium “D-lines” are at 589.00 nm and 589.59 nm. Resolving them corresponds to resolvance

Another standard example is the resolution of the hydrogen and deuterium lines, often done with a Fabry-Perot Interferometer. The red lines of hydrogen and deuterium are at 656.3 nm and 656.1 nm, respectively. This requires a resolvance of

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