d(uv) = u dv + v du

where:

v = [exp(c_{2}/( T) -1)]^{-1}

We need to take the derivative of this term. There are two possibilities:

- as an expression raised to a power: v = Z
^{t}where dv = t Z^{t - 1}dZ or - as a fraction : v = 1/Z where dv = [Z × d(1) - 1 × dZ]/Z
^{2}

**Case 1** here the power, t, equals -1. Immediately we have dv =
-1 [exp(c_{2}/( T) -1)]^{-2} dZ. Now we must find the
derivative of the exponential term. The devivative of an exponential
is simply the exponential term itself multiplied by the derivative of the
exponent. In this case, since we are taking the derivative with respect to
wavelength, , the derivative of the exponent is _{2}/^{2} T]exp(c_{2}/( T).

dv = [c_{2}/(^{2} T)] [exp(c_{2} /T)/(exp(c_{2} /T) - 1)^{2}].

**Case 2:** the derivative of 1, a constant, is 0, so the first term
in the numerator drops out. For the second term, we must again know what the
derivative of exp(c_{2}/( T) - 1) is.
Using our result above,
combining these terms (and noticing that they will be multiplied by -1),
we again get the expression below.

dv = [c_{2}/(^{2} T)] [exp(c_{2} /T)/(exp(c_{2} /T) - 1)^{2}].

Not surprisingly, they are identical.

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.