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Relativistic Doppler Shift Using Wavelength

The relativistic Doppler effect is the change in wavelength of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity.

The ratio of the wavelength at the source and the wavelength observed equals the square root of the speed of light minus the speed of the source away from the observer divided by the speed of light plus the speed of the source away from the observer.

Formula

QuantityVariable[Subscript["λ", "s"], "Wavelength"]/QuantityVariable[Subscript["λ", "o"], "Wavelength"] == Sqrt[(Quantity[None, "SpeedOfLight"] - QuantityVariable[Subscript["v", "s"], "Speed"])/(Quantity[None, "SpeedOfLight"] + QuantityVariable[Subscript["v", "s"], "Speed"])]

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Relativistic Doppler Shift Using Wavelength"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject["Relativistic Doppler Shift Using Wavelength"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Relativistic Doppler Shift Using Wavelength"], {QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("s"\)]\),"Speed"] -> Quantity[0.22`, "SpeedOfLight"], QuantityVariable[ \!\(\*SubscriptBox[\("\[Lambda]"\), \("o"\)]\),"Wavelength"] -> Quantity[687.5`, "Nanometers"]}]
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