L12 Thermal Radiation

L12 Thermal Radiation#

Week 6, Thursday

Material covered and references#

Properties of “blackbodies” objects. From the energy distribution of photon inside of the BB cavity, we found:

  • The total energy density

  • The distribution of photon’s frequency and wavelength (beware of the conversion)

  • That the intensity of the light inside the cavity was equal to the Planck function

  • that the flux inside of the cavity is zero

  • that the flux at the surface of a BB (light going through the “hole”) is \(\sigma T^4\).

In the textbooks:

  • LeBlanc Special Topic eqs 3.19-3.21

  • Grey Chapter 6

  • Hansen sec 3.2

  • In the case of a pure thermal radiation at a single temperature, there is no change in intensity such that \(S_\lambda = I_\lambda\).

  • But in the case of LTE, the temperature gradient means that the intensity \(I_\lambda\) is not always \(B_\lambda\), if the source function changes within a few optical depths. However, locally the source function can be approximated by \(S_\lambda \simeq I_\lambda\) if scattering processes are much less important than pure absorption processes.

In the textbooks:

  • Leblanc section 3.5

We explored the frequency dependence of the opacity and its effect on the frequency dependence of the intensity exiting a slab of material with \(S_\lambda=B_\lambda(T)\). We can link these with the type of spectra described by the Kirchhoff’s law of spectroscopy. https://en.wikipedia.org/wiki/Gustav_Kirchhoff#Kirchhoff.27s_three_laws_of_spectroscopy