### Rayleigh-Jeans law

(Raleigh-Jeans limit, Raleigh-Jeans approximation)
(yields approximation of black body curve useful at low frequencies)

The Rayleigh-Jeans law is a formula that approximates black-body radiation at longer wavelengths, i.e., approximates one of the two tails of the spectrum, which is precisely specified by the Planck function. The Raleigh-Jeans law has the advantage of being a simpler function, easier to manipulate algebraically and incorporate into formulae describing astronomical phenomena. The Rayleigh-Jeans law and the Wien approximation are analogous, each approximating one end of a black-body spectrum. Its form based upon wavelength:

```Bλ(T) = 2cKBT/λ4
```

Or, based upon frequency, giving a SED according to frequency-differentials:

```Bν(T) = 2ν²KBT/c²
```
• ν - frequency.
• Bν(T) - analogous SED, for frequency instead of wavelength.

Being a good approximation of the spectrum's longer-wavelength tail, it is useful in radio astronomy. The longer the wavelength, i.e., further toward that tail, the closer together they are, and the spectrum produced by the law is known as the Rayleigh-Jeans limit, a curve that the actual black body spectrum approaches. The region of the spectrum where this is a useful approximation is called the Rayleigh-Jeans regime or Raleigh-Jeans region. The this regime's location depends upon the temperature-regime: the hotter the type of objects, the more the Rayleigh-Jeans regime extends toward shorter wavelengths.

The Rayleigh-Jeans law was devised before the Planck function was known and was derived from classical (pre-quantum mechanics) physical principles by Lord Rayleigh and James Jeans. However, it was clearly wrong: it says that the shorter the wavelength, the more electromagnetic radiation is emitted at that wavelength, approaching infinity. Among other issues, this would imply objects would cool to zero in zero time. This anomaly between theory and observation is termed the ultraviolet catastrophe. The Planck function matched observation and quantum mechanics developed from the physical rules this implied.

(function,physics,EMR,black body)