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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 NA is derived from the size of the lens, its working distance, and it's index of refraction. High-quality objective lenses indicates their Numerical Aperture on the sides of their barrels. In general, the useful magnification of an objective is 1000 times its Numerical Aperture.