Where f ¼ c/l is the frequency, Hz; (c ¼ 2.9996 Á 10
14
mm/s is the light
velocity).
Throughout most of the shortwave range l < 2 mm for Earth self heat radiation
the exponential term is larger than one, thus Wien approximation is obeyed by the
blackbody spectral brightness:
B n ðTÞ ¼ an
3 exp À
b n
T
(2.4)
For long waves (l >100 mm) Rayleigh-Jeans approximation is true for the
blackbody spectral brightness:
B n ðTÞ ¼ ða=bÞn
2 T:
(2.5)
After integrating the Planck’s function over all wave numbers (wavelengths,
frequencies) the blackbody irradiance F(T) is obtained.
FðTÞ ¼ sT
4
(2.6)
The Eq. 2.6 is called Stefan-Boltzmann law, where s ¼5.6693 Á 10
À8
, W/(m
2
Á
K
4
)
is the Stefan-Boltzmann constant.
0
500
1000
1500
2000
2500
0
5
10
15
20
25
Wavelength, mkm
Spect ral brigthness, W m
-2
mkm
-1
T=800
T=500
Fig. 2.1 Planck’s function for two temperatures 800 and 500
K
2.2 Basic Equations
21