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The numerical aperture of a microscope objective defines the objective's resolution. Each microscope objective has a minimum and maximum magnification necessary for the details in an image to be resolved. A simple formula for the minimum value is (500 x NA). And for the maximum magnification (1000 x NA).
The numerical aperture (NA) of the fiber is the sine of the maximum angle of an incident ray with respect to the fiber axis, so that the transmitted beam is guided in the core. The NA is determined by the refractive index difference between core and cladding, more precisely by the relation.