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Fabry–Pérot Interferometer Using Plate Reflectance

This formula describes the transmission and reflection of light through a Fabry­Pérot interferometer, or etalon, a transparent plate with two reflecting surfaces or two parallel, highly reflecting mirrors.

Interferometer transmittance varies inversely with the sine of the product of the plate spacing, the index of refraction, the reciprocal of the wavelength and the cosine of the angle of incidence. Increasing the plate reflectance tends to decrease transmittance. Interferometer reflectance is 1 minus the transmittance.

Formula

{QuantityVariable[Subscript["T", "e"], "Unitless"] == (1 - QuantityVariable["R", "Unitless"])^2/(1 - 2*Cos[(4*Pi*Cos[QuantityVariable["θ", "Angle"]]*QuantityVariable["l", "Distance"]*QuantityVariable["n", "Unitless"])/QuantityVariable["λ", "Wavelength"]]*QuantityVariable["R", "Unitless"] + QuantityVariable["R", "Unitless"]^2), QuantityVariable[Subscript["R", "e"], "Unitless"] == 1 - QuantityVariable[Subscript["T", "e"], "Unitless"]}

symbol description physical quantity
Te interferometer transmittance "Unitless"
R plate reflectance "Unitless"
θ angle of incidence "Angle"
l plate spacing "Distance"
n index of refraction between plates "Unitless"
λ wavelength "Wavelength"
Re interferometer reflectance "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Fabry\[Dash]Pérot Interferometer Using Plate \ Reflectance"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Fabry\[Dash]Pérot Interferometer Using Plate Reflectance"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Fabry\[Dash]Pérot Interferometer Using Plate Reflectance"], \ {QuantityVariable["n","Unitless"] -> 1.33`, QuantityVariable["\[Lambda]","Wavelength"] -> Quantity[532, "Nanometers"], QuantityVariable[ \!\(\*SubscriptBox[\("R"\), \("e"\)]\),"Unitless"] -> 0.1`}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1899

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