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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. The entire spectrum is precisely specified by the Planck function, and the Rayleigh-Jeans law constitutes one possible Taylor-expansion-based approximation of that function. The Rayleigh-Jeans law has the advantage of being a simpler function, easier to manipulate algebraically and incorporate into formulae describing astronomical phenomena. It is also simpler than the Wien approximation, which analogously approximates the shorter-wavelength tail of a black-body spectrum. The Rayleigh-Jeans law based upon wavelength:
Bλ(T) = 2cKBT/λ4
Or, based upon frequency, yielding a spectral energy distribution (SED) according to frequency-differentials:
Bν(T) = 2ν²KBT/c²
Much of astrophysics uses the term intensity for the quantity of radiation emitted through a surface into a given solid angle, specific intensity being the intensity at a given wavelength or frequency. More common terms are radiance and spectral radiance.
Being a good approximation of the spectrum's longer-wavelength tail, the Rayleigh-Jeans law is useful in radio astronomy. With increasing wavelength, the Rayleigh-Jeans law's curve approaches that of the black-body spectrum, and it is known as the black-body spectrum's Rayleigh-Jeans limit. The region of the spectrum where the Rayleigh-Jeans law is a useful approximation is called the Rayleigh-Jeans regime, Rayleigh-Jeans region, or Rayleigh-Jeans tail. The regime's extent depends upon the temperature-regime: the hotter the object, the further the Rayleigh-Jeans regime extends toward shorter wavelengths. The regime's high-frequency limit is not exact: any precise specification would depend upon how close an approximation you require.
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 EMR 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.