colour.colorimetry.rayleigh_jeans_law#

colour.colorimetry.rayleigh_jeans_law(wavelength: ArrayLike, temperature: ArrayLike) → NDArrayFloat[source]#

Return the approximation of the spectral radiance of a blackbody as a function of wavelength at thermodynamic temperature \(T[K]\) according to Rayleigh-Jeans law.

Parameters:

  • wavelength (ArrayLike) – Wavelength in meters.

  • temperature (ArrayLike) – Temperature \(T[K]\) in kelvin degrees.

Returns:

Radiance in watts per steradian per square metre (\(W/sr/m^2\)).

Return type:

numpy.ndarray

Warning

The colour.colorimetry.rayleigh_jeans_law() definition behaviour with n-dimensional arrays is unusual: The wavelength and temperature parameters are first raveled using numpy.ravel(). Then, they are broadcasted together by transposing the temperature parameter. Finally, and for convenience, the return value is squeezed using numpy.squeeze().

Notes

  • The Rayleigh-Jeans law agrees with experimental results at large wavelengths (low frequencies) but strongly disagrees at short wavelengths (high frequencies). This inconsistency between observations and the predictions of classical physics is commonly known as the ultraviolet catastrophe.

  • The following implementation is expressed in terms of wavelength.

  • The SI unit of radiance is watts per steradian per square metre (\(W/sr/m^2\)).

References

[Wikipedia03e]

Examples

>>> rayleigh_jeans_law(500 * 1e-9, 5500)  
728478884562351.5...
>>> rayleigh_jeans_law(500 * 1e-9, [5000, 5500, 6000])
... 
array([  6.6225353...e+14,   7.2847888...e+14,   7.9470423...e+14])