The resolving power of microscopes is the ability of a microscope, telescope, or other optical instrument to produce separate images of closely placed objects. These microscopes can be light and electron microscopes. The resolving power of a microscope is ultimately limited by the wavelength of the probe, e.g. electron and light beams. Furthermore, the resolving power of the measurements is fundamentally determined by the bigger volume irradiated by the incident electron beam or from which the stimulated signal arises. The first estimation of the spatial resolution of a microscope can be given by,
Resolution ≈ ½λ --------------------------- 
λ -- The wavelength which is used, e.g. wavelength of lights and wavelength of electrons.
On the other hand, the resolving power of spectrometers is the ability of a spectrometer to separate two adjacent peaks in a spectrum. Figure 4563 shows the resolving power of different microscopes over the last 200 years. The resolving power of the microscopes has been improved by introducing EMs (electron microscopes) and consequent field emission gun and Cs and Cc correctors.
Figure 4563. The resolving power of different microscopes over the last 200 years (; Adapted from [2 - 3] ).
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 Muller, D. A. (2009). Structure and bonding at the atomic scale by scanning transmission
electron microscopy. Nature Materials, 8, 263–270.
 Rose, H. H. (2009). Historical aspects of aberration correction. Journal of Electron Microscopy
(Tokyo), 58, 77–85.