Textbooks often present spectral distribution functions (spectra) versus wavelength, whereas spectroscopists are likely to present them versus wavenumber (frequency). Consequently, these different representations of spectra, which are rarely juxtaposed, can lead to apparent contradictions if they are. Heald1 showed that the peak of the Planck function depends on how it is plotted; there are several choices, all equally valid. Planck2 himself noted “that in a certain spectrum [plotted versus wavelength and frequency]…the maxima lie at different points.” This is true for the Planck and other broad spectra, and differences can be appreciable (a factor of about two). But atomic spectroscopists need not fret because the positions of narrow spectral lines are independent of the representation to good approximation (the shift is approximately the relative line width squared). What about the width (at half maximum) of the peak of the Planck function? In the frequency representation it increases with increasing temperature, whereas in the wavelength representation it decreases. But the width relative to the peak is independent of temperature and narrower in the wavelength representation. These points are neither profound nor difficult to show, but I have never found them all together, hence the motivation for this letter to which I add the related aside.

Assertions that at high temperatures blackbody radiation appears blue are true if by high is meant >10,000 K and the radiation is greatly attenuated lest the observer be blinded. But obtaining solid or liquid real bodies this hot would be daunting given that the boiling point of tungsten is 5800 K. The perceived color (chromaticity coordinates) of a real incandescent body depends on the integrated product of its spectral emissivity and the Planck function (i.e., its emission spectrum), which is independent of representation. The emissivity of solids and liquids often does not vary greatly over the visible (e.g., that for iron3 varies about 40%), whereas for incandescent gases it often varies appreciably with wavelength and temperature. Yet in Ref. 4 I find the following: “at higher [blackbody] temperatures still, the maximum of the curve shifts further to shorter wavelengths, so that the light emitted appears bluish—as is seen in the electric arc used for welding.” If an electric arc (or flame) is perceptually blue, this is not because its thermodynamic temperature is >10,000 K. The much colder bluish flame of a propane stove burner originates from Swan bands.5 The correlated color temperature of visible light sources—the (approximate) temperature of a blackbody with the same perceived color but not necessarily the same luminance—is often markedly different from their thermodynamic temperature. For example, the correlated color temperature of daylight and skylight ranges from 3000 K to 106 K (Ref. 6). Fortunately, we need not fear of being burned to a crisp under a vivid blue sky.

1.
Mark A.
Heald
, “
Where is the Wien peak?
,”
Am. J. Phys.
71
(
12
),
1322
1323
(
2003
).
2.
Max
Planck
,
The Theory of Heat Radiation
(
Dover
,
New York
,
1959
), p.
16
.
3.
Jack Eldon
Taylor
, “
The variation with wavelength of the spectral emissivity of iron and molybdenum
,”
J. Opt. Soc. Am.
42
(
1
),
33
36
(
1952
).
4.
O. S.
Heavens
,
Lasers
(
Charles Scribner & Sons
,
New York
,
1971
), p.
15
.
5.
Swan's 1857 paper, well worth reading, is accessible at http://en.wikipedia.org/wiki/Swan_band.
6.
Javier
Hernández-Andrés
,
Raymond
Lee
, Jr.
, and
Javier
Romero
, “
Calculating correlated color temperature across the entire gamut of daylight and skylight chromaticities
,”
Appl. Opt.
38
,
5703
5704
(
1999
).