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Numerical Aperture Using Aperture Diameter

The numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.

The numerical aperture decreases inversely with focal length. As the diameter of the aperture increases, the numerical aperture approaches 1 over twice the focal length. As it decreases, so does the numerical aperture.

Formula

QuantityVariable["NA", "Unitless"] == QuantityVariable["D", "Diameter"]/(2*Sqrt[1 + QuantityVariable["D", "Diameter"]^2/(4*QuantityVariable["f", "Length"]^2)]*QuantityVariable["f", "Length"])

symbol description physical quantity
NA numerical aperture "Unitless"
D diameter of aperture "Diameter"
f focal length "Length"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Numerical Aperture Using Aperture Diameter"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Numerical Aperture Using Aperture Diameter"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Numerical Aperture Using Aperture Diameter"], {QuantityVariable[ "NA","Unitless"] -> 0.1`}]
Out[3]=

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