Black body radiation and color temperature

Every object radiates electromagnetic radiation which is not visible at ambient temperature. The spectrum of this radiation is not dependent on the chemical composition of the object, but only on its temperature T. The spectrum has a bell shape and its maximum is proportional to 1/T and the emitted energy (integral of the curve) is proportional to T4. as described in the figure below:

Back body radiation spectrum at 6'000 K, 5'000 K, 4'000 K and 3'000 K

If the temperature is increased the average radiated wavelength becomes shorter and at temperatures around 1'000 K part of the radiation becomes visible since wavelengths in the 700 nm region are present and the object appears "red hot" as shown in the figure below which is actually a "zoom" of the previous chart calculated at different temperatures.

Back body radiation spectrum at 1'200 K, 1'100 K, 1'000 K and 900 K

At higher temperatures the color of the radiation will tend to yellow, white and white-blue, roughly according to the table below. Please keep in mind that color perception is subjective and different authors report slightly different colors.

1'000 K      Red
1'500 K      Reddish orange
2'000 K      Yellowish orange
2'800 K      Yellow
4'500 K      White
10'000 K      Blue white

The equation that gives these spectrums was discovered by Plank and is:

u(lambda,T)=(8*pi*h*c/(lambda^5))*1/(e^(h*c/(lambda*k*T))-1)      c=2.998E8 m/s
1.381E-23 J/K
6.6256E-34 J*s

The maximum of the distribution is given by the "Wein's shift":

lambda_max=2.898E-3[mm*K]/T

Since hot bodies are very often used as light sources color temperature is used to describe the color of the light. For example the sun, a filament light bulb, a candle, and many other light sources can be considered as "black body" radiators.

Color temperature in photography is simply measured by comparing the blue and red components of the light without exactly measuring its spectrum, but it's still measured in Kelvins and values are very similar to the temperature of a black body.

The following table gives a few examples of the color temperature of some light sources:

1'500 K      Candlelight
2'700 K      Incandescent lamp
3'200 K      Sunrise / sunset
3'400 K      Halogen incandescent lamp
5'500 K      Sunny daylight around noon
6'000 K      Electronic photo flash
7'000 K      Overcast sky
10'000 K      Blue sky

Home Optics 08561 Last update: 01/12/04