Revision 41432 of "Numerical_aperture" on enwiki

For [[optical fibre]] as used in [[telecommunication]], '''numerical aperture''' (<i>NA</i>) has the following meanings: 

<b>1.</b>  The sine of the [[vertex angle]] of the largest cone of meridional rays that can enter or leave an optical [[system]] or element, multiplied by the [[refractive index]] of the [[medium]] in which the vertex of the cone is located. 

<i>Note:</i>  The <i>NA</i> is generally measured with respect to an object or image point and will vary as that point is moved. 

<b>2.</b>  For an [[optical fiber]] in which the [[refractive index]] decreases monotonically from <i>n</i> <sub>1</sub> on the axis to <i>n</i> <sub>2</sub> in the [[cladding]], an expression of the extent of the fiber's ability to [[accept]], in its bound modes, non-normal incident rays, given by <i>NA</i> = (<i>n</i> <sub>1</sub><sup>2</sup>-<i>n</i> <sub>2</sub><sup>2</sup>)<sup>&frac12;</sup>. 

<i>Note:</i>  In multimode fibers, the term <i>equilibrium numerical aperture</i> is sometimes used. This refers to the numerical [[aperture]] with respect to the extreme exit angle of a [[ray]] emerging from a fiber in which [[equilibrium mode distribution]] has been established.  

<b>3.</b>  <i>Colloquially,</i> the sine of the radiation or [[acceptance angle]] of an optical fiber, multiplied by the refractive index of the material in contact with the exit or entrance face. 

<i>Note:</i>  This usage is approximate and imprecise, but is often encountered.

Source: from [[Federal Standard 1037C]] and from [[MIL-STD-188]]
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In [[microscopy]], the '''numerical aperture''' (<math>A_N</math>) of an [[lens|objective]] is:

<center>
<math>A_N = I \sin \frac {a} {2}</math>
</center>

where <math>I</math> is the [[index of refraction]] of the medium in which the lens is working (1.0 for [[air]], up to 1.56 for [[oil]]s), and <math>a</math> is the [[angular aperture]] of the [[lens]]. The numerical aperture basically is a measure of the diameter of the [[aperture]] compares to the [[focal length]]. In [[photography]], the [[f-number]] expresses the same relationship.