## 1. Black Body Emissive Power (Planck's Law) Max Plank formulated the [[Emissive Power]] for a black body $E_{b\nu}(T,\nu) = \frac{2\pi h \nu^3n^2}{c_0^2[e^{hc_0/n kT}-1]}$ where $n$ is refractive index of the medium bounding the black body $k = 1.3807 \times 10^{-23}$ J/k (Boltzmann's constant) the equation is also written in terms of wavelength $\lambda$ If you integrate above equation for all wavelength, you get Stefan Boltzmann's law Wien's law and Rayleigh Jeans law can be derived from Planck's law applying certain assumptions and approximations. ## 2. Fractional black body emissive power is the emissive power of a black body in a range of wavelengths as a function of overall blackbody emissions. Plank's law plotted looks like [this](https://en.wikipedia.org/wiki/Black-body_radiation). (Black line is the Rayleigh Jeans ultraviolet catastrophe described [[Radiation-Historical Perspective|here]]) The blue line is approximately what the sun emits. But when the earth receives it the gases in the atmosphere absorb various frequencies (which change depending on time of they day) [[Radiation-Historical Perspective]]