Light - Computer Graphics: Principles and Practice - page 672

The simple model of discrete energy levels really applies only to an isolated
atom. When multiple atoms are in proximity (as in solids), each individual energy
level available to electrons gets “spread out” into a band of energies. Still, elec-
trons can generally absorb or release energies only when the amount absorbed or
released represents the difference of two energies in the bands.
In some materials—like metals—certain electrons are not attached to partic-
ular nuclei, but can instead move about the material, helping to make the mate-
rial conductive. These electrons have a great many possible energy states, and
therefore can absorb photons of many different wavelengths and then promptly
emit them again. This generally makes conductive materials like metals reflective,
while most transparent materials are insulators.
In other materials—like some forms of carbon—there are also unattached
electrons, but they cannot move quite as freely. Such an electron can interact with
atoms of the material, causing those atoms to move and vibrate while the elec-
tron loses energy. This motion of atoms is called heat. Thus, materials like soot
tend to absorb photons, and rather than reemitting the photons, they convert them
into heat. This is why soot looks black, and why dark clothes heat up on a sunny
day. Note that light of all frequencies is convertible to heat. In particular, infrared
light (light of wavelengths slightly longer than those we can see) is a kind of elec-
tromagnetic radiation, just like the light we see; it happens to be more readily
convertible to heat than is visible light, but it's still light.
In the exact reverse process, if we heat up soot, the atoms vibrate; this vibra-
tion in turn may “kick around” a loose electron, causing it to have excess energy,
which it may lose by emitting a photon. Because of the many possible energy
states for the loose electron, the emitted light can have many possible energies
(wavelengths). Thus, materials that are good at absorbing energy and converting
it to heat are also good at emitting energies of many different amounts when they
are heated.
As materials are heated, they all become increasingly better at emitting elec-
tromagnetic radiation. Indeed, all bodies at all temperatures above absolute zero
actually emit some radiation, but at the low temperatures we encounter in ordinary
life, it's not very much. We mostly see things because they are reflecting light
rather than because they are emitting it themselves. The exceptions are things like
the filaments in incandescent lightbulbs, hot metal being forged by a blacksmith,
or the sun.
We can measure the energy radiated by an object heated to temperature T (see
Figure 26.3). For each narrow range of wavelengths, we can measure the energy
radiated in that range; plotting this function I (

gives a
graph like that shown in Figure 26.4. At very low temperatures, such measure-
ments are easily confounded with reflected energy. But if we imagine an ideal
black body —one that can absorb and emit electrons as well as possible—in a
room in which the only energy is in the form of heat, we get a plot like the one
shown in the figure.
The dependence of I on T can be measured; the total power radiated depends
on the fourth power of T :

λ , T ) against frequency λ

T 4 , where 10 − 8 Wm − 2 K − 4 ;

power = σ σ = 5.67 ×

this is known as the Stefan-Boltzmann law. (The K in this expression denotes
“degrees Kelvin.”)