5.3
The spectral irradiance I eν or I eλ is calculated similarly. The physical dimensions are
[I e ] = W
m−2
, [I eν ] = Wm
−2
s, [I eλ ] = Wm
−2
m
−1
.
The irradiance also is given as
and similarly for I eν and I eλ . Irradiance refers to radiation that is received by the surface.
For radiation emitted by the surface, we instead speak of radiant emittance, M e , M eν , and
M eλ .
As we discussed earlier, the energy of a photon is proportional to its frequency, E ph =
hν = hc/λ. Thus, the spectral power P λ is proportional to the spectral photon flow Ψ ph, λ,
and similarly for P ν and Ψ ph,ν . The total photon flow Ψ ph is related to the spectral photon
flow via
The physical dimensions of the (spectral) photon flow are
[Ψ ph ] = s
−1 , [Ψ ph, ν] = 1, [Ψ ph, λ] = s
−1
m
−1
.
The (spectral) photon flux Φ ph is defined as the photon flow per area,
and similarly for Φ ph, ν and Φ ph, λ. The physical dimensions are
[Φ ph ] = s
−1
m
−2 , [Φ ph, ν] = m
−2
, [Φ ph, λ] = s
−1
m
−2
m
−1
.
By comparing Eqs. (5.11) and (5.14) and looking at Eq. (5.12), we find
and analogously for I eν and Φ ph, ν.
Blackbody radiation
If we take a piece of metal, for example, and start heating it up, it will start to glow, first in
a reddish colour, then getting more and more yellowish as we increase the temperature
even further. It thus emits electromagnetic radiation that we call thermal radiation.