EME 810
Solar Resource Assessment and Economics

3.3. Four Laws of Light

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Reading Asignment

  • J.R. Brownson, Solar Energy Conversion Systems (SECS), Chapter 3: Laws of Light

We continue our review of the seven basic rules, or "laws," of light. These four are a bit closer to physical laws than what's on the prior page, but we need to understand the basics of light if we are to move on to the physics of light interacting with the atmosphere.

You may want to use the math/science site Wolfram Alpha to solve several of these Self-Test questions quickly, or to check some of the notes in Wolfram Alpha against our own work here. Wolfram Alpha is the Google of math and physics. If you want to do calculations on Wien's Law, you type "wien's law" and you will get a calculator for Wien's Law with all sorts of other information.

Kirchoff's Law

This radiative transfer law is very important when considering energy balance. It states that at thermal equilibrium, the emissivity ( ϵ) of a body or surface equals its absorptivity ( α).

Mathematically, we can conceptualize Kirchoff's law as

E E b =ϵ=α

The radiant energy emitted from a real surface is represented as E (W/m2), while that of a blackbody (a theoretical condition) is given by EB (W/m2).

Simply put, a surface at steady state temperature will absorb light equally as well as it emits light. Though light is directional, surfaces exchange photons in both directions.

Self-check question:

 The human body has an emittance ( ϵ) of about 0.85 for the longwave band and shortwave band. What is the absorptance of your skin in the shortwave band? 

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ANSWER: For the temperature of the human body in near equilibrium with its surroundings α=ϵ=0.85 . This also means we only reflect about 15% of the light incident on our skin.

Planck's Law

This law is generalized to mean that all objects have some internal temperature, and given that temperature, they all glow. Max Planck was able to establish the dependence of the spectral emissive energy of a blackbody for all wavelengths of light ( E λ,b), given a known equilibrium temperature of the blackbody.

E λ,b = 2πh c 2 λ 5 [ e hc λKT 1]

Wien's Displacement Law

The Wien's displacement law provides us with expected values for the most probable wavelengths in the Bose-Einstein distribution of blackbody radiation. The law implies that the distribution of photons emitted from a surface at any temperature will have the same form or shape as a distribution of photons emitted from a surface at any other temperature. Mathematically,

λ max = 2.8978× 10 6 nmK T(K)

Self-check questions:

1. The human body "glows" at about 310K, making the most probable wavelength (from Wien's Law) about 9,300 nm. What is that in terms of eV?

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ANSWER: 9300 nm is about 0.1 eV
 

2. The Sun "glows" at about 5777K. What is the most probable wavelength, and the value of the wavelength in terms of eV?

Click for answer.

ANSWER: Going to Wolfram Alpha and searching "Wien's displacement law," we find λ max 500 nm . This is about 2.5 eV in energy for that single wavelength.
 

Stefan-Boltzmann Law

The Stefan-Boltzmann Law states that the radiative energy emitted by a surface is proportional to the fourth power of the surface's absolute temperature. The Stefan-Boltzmann Law shows that if you were to integrate all the energies from the wavelengths in Planck's Law, you have an analytical solution of the form below:

E b = 0 E λ,b dλ=σ T 4

where σ = Stefan-Boltzmann constant 5.67× 10 8W/ m 2 K 4

Keep in mind that this is for the surface of the emitter. A surface like the Sun will have a very high value for the energy density on the surface, which then decreases in proportion with the Inverse Square Law from the last page (over the 93 million miles distance to Earth's surface).