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Optical magnification is the ratio between the apparent size of an object (or its size in an image) and its true size, and thus it is a dimensionless number. Optical magnification is sometimes referred to as "power" (for example "10× power"), although this can lead to confusion with optical power.
[3] [5] The magnification here is typically negative, and the pupil magnification is most often assumed to be 1 — as Allen R. Greenleaf explains, "Illuminance varies inversely as the square of the distance between the exit pupil of the lens and the position of the plate or film. Because the position of the exit pupil usually is unknown to the ...
where N is the uncorrected f-number, NA i is the image-space numerical aperture of the lens, | | is the absolute value of the lens's magnification for an object a particular distance away, and P is the pupil magnification. Since the pupil magnification is seldom known it is often assumed to be 1, which is the correct value for all symmetric lenses.
Traditional depth-of-field formulas can be hard to use in practice. As an alternative, the same effective calculation can be done without regard to the focal length and f-number. [b] Moritz von Rohr and later Merklinger observe that the effective absolute aperture diameter can be used for similar formula in certain circumstances. [19]
A calculation using Airy discs as point spread function shows that at Dawes' limit there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip. [3] Modern image processing techniques including deconvolution of the point spread function allow resolution of binaries with even less angular separation.
Magnification and demagnification by lenses and other elements can cause a relatively large stop to be the aperture stop for the system. In astrophotography , the aperture may be given as a linear measure (for example, in inches or millimetres) or as the dimensionless ratio between that measure and the focal length .
This magnification formula provides two easy ways to distinguish converging (f > 0) and diverging (f < 0) lenses: For an object very close to the lens (0 < S 1 < | f |), a converging lens would form a magnified (bigger) virtual image, whereas a diverging lens would form a demagnified (smaller) image; For an object very far from the lens (S 1 ...
When the magnification is small, the formula simplifies to t ≈ 2 N c . {\displaystyle t\approx 2Nc.} The simple formula is often used as a guideline, as it is much easier to calculate, and in many cases, the difference from the exact formula is insignificant.