====== Blackbody ======
A blackbody refers to an idealized object or system that absorbs all incident electromagnetic radiation, regardless of its frequency or wavelength.

A blackbody is never black, it always emits light and the wavelength of the light depends only on its temperature.

Planck's law describes the [[surface brightness]] of a blackbody at a specific temperature $T$ as a function of frequency or wavelength. Surface brightness as a function of frequency $\nu$

$$ S_\nu = \frac{2h\nu^3}{c^2} \frac{1}{e^{h\nu/(kT)}-1} $$

where $h$ is [[Planck constant]], $k$ is [[Boltzmann constant]], $c$ is the [[speed of light]] and $e$ is [[Euler's number]]. The quantity is plotted below.

[[https://colab.research.google.com/drive/1vhrIuzj8mA5RnksjLuWGsPMko6J993gi?usp=sharing|{{:courses:ast201:blackbody-nw-thz.png?nolink&570}}]]

The surface brightness as a function of wavelength $\lambda$

$$ S_\lambda = \frac{2hc^2}{\lambda^5} \frac{1}{e^{hc/(\lambda kT)}-1} $$

and this [[quantity]] is plotted below for three different temperatures.

[[https://colab.research.google.com/drive/1vhrIuzj8mA5RnksjLuWGsPMko6J993gi?usp=sharing|{{:courses:ast201:blackbody-kW-nm.png?nolink&570}}]]