Page 290 - Modern Optical Engineering The Design of Optical Systems

Principles of Radiometry and Photometry 269

Figure 12.7 The total emissivity of a number of materials.

When dealing with gray-bodies, it is necessary to insert the emis-
sivity factor into the blackbody equations. Planck’s law (Eq. 12.14),
the Stefan-Boltzmann law (Eq. 12.15), and the Wien displacement law
(Eq. 12.17) should be modified by multiplying the right-hand term by
the appropriate value of . For many materials the emissivity is a func-
tion of wavelength. This is apparent from the fact that many substances
(glass, for example) have a negligible absorption, and consequent low
emissivity, at certain wavelengths, while they are almost totally
absorbent at other wavelengths. In regions of the spectrum where this
occurs, emissivity becomes spectral emissivity ( ) and is treated just
as any other spectral function. For many materials, emissivity will
decrease as wavelength increases. It should also be noted that most
materials show a variation of emissivity with temperature as well as
wavelength, and precise work must take this into account. Emissivity
usually increases with temperature.