F = 2 h c^{2} ^{-5} / (exp(hc/kT) - 1).

or, combining the constants:

F = c_{1} ^{-5} / exp(c_{2} /T) - 1),

where c_{1} = 2 hc^{2} = 3.7419 × 10^{-5} erg cm^{2} s^{-1} [ in cm]

and c_{2} = hc/k = 1.4288 cm °K.

On the red side of the distribution (when T >> 1)
the denominator approaches zero as x => 0 and e^{x} => 1. For small values
of the exponent, the series expansion for the exponential can be used as
an excellent approximation of the value of the exponential.

e^{x} = 1 + x + x^{2}/2! + x^{3}/3! + x^{4}/4! + . . .

But when x is very small, all terms beyond the first in x can be ignored, allowing us to use:

e^{x} = 1 + x

Making this substitution, we obtain:

F = c_{1} ^{-5} / (1 + c_{2} /T - 1),

or:

F = (c_{1}/c_{2}) T ^{-4}.

This expression for the blackbody distribution on the red side of the
maximum of the Planck curve is called the **Rayleigh-Jeans Distribution**.

Introduction to Blackbody radiation

Wien Distribution

Wien Displacement Law

Stefan-Boltzmann Law

Constants

This VRML + HTML package on Blackbody emission was constructed by Karen M. Strom. Contact your local instructor for help if it is used as part of your class.