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Principles of Radiometry and Photometry 265

to known laws, and since it is possible to build a close approximation to
an ideal blackbody, a device of this type is a very useful standard source
for the calibration and testing of radiometric instruments. Further, most
sources of thermal radiation, i.e., sources which radiate because they are
heated, radiate energy in a manner which can be readily described in
terms of a blackbody emitting through a filter, making it possible to
use the blackbody radiation laws as a starting point for many radio-
metric calculations.
Planck’s law describes the spectral radiant emittance of a perfect
blackbody as a function of its temperature and the wavelength of the
emitted radiation.
C
1
W (12.14)
5 C 2 / T
(e 1)
where W the radiation emitted into a hemisphere by the blackbody
in power per unit area per wavelength interval (W cm 2
m )
1
the wavelength ( m)
e the base of natural logarithms (2.718…)
T the temperature of the blackbody in Kelvin (K °C 273)
4
C 1 a constant 3.742 10 when area is in square centime-
ters and wavelength in micrometers
4
C 2 a constant 1.4388 10 when square centimeters and
micrometers are used
Figure 12.6 indicates the shape of the curve of W plotted against
wavelength. Note that the spectral radiance (N ) is given by W / .
If we integrate Eq. 12.14, we can obtain the total radiation at all
wavelengths. The resulting equation is known as the Stefan-
Boltzmann law,
4
W 5.67 10 12 T W/cm 2 (12.15)
TOT
and indicates that the total power radiated from a blackbody varies as
the fourth power of the absolute temperature.
If we differentiate Planck’s equation (12.14) and set the result equal
to zero, we can determine the wavelength at which the spectral emit-
tance (W ) is a maximum and also the amount of W at this wavelength.
Wien’s displacement law gives the wavelength for maximum W as
2897.8T 1 m (12.16)
max
and W at max as

5
2
W 1.286 10 15 T W/cm m 1 (12.17)
, max