Spectral Distribution of Radiant Energy

Planck's law enables us to determine the complete spectral distribution of energy emitted by a black body at different temperatures at various wave-lengths. Prevost's finding that in the physical world, every body, regardless of its surroundings and temperature, emits its own radiation makes it possible for us to examine the characteristic spectrum of radiation from any body of interest to us. In fact, the spectral analysis has been used widely as a powerful tool to examine the physical conditions of radiating bodies in almost all branches of science. Since, in the present book, we are mainly concerned with the radiation emitted by the sun and the earth-atmosphere system, let us examine Fig. 6.1, reproduced from Brunt (1944).

Figure 6.1 which shows the spectral distribution of energy radiated at the temperature of the sun (T = 6,000K) as well as those of the earth's troposphere (T = 300K) and stratosphere (T = 200K), as determined from Planck's law, assuming that they all radiate energy as a black body at their respective temperatures. From it, it is evident that although the horizontal scale has been designed to ensure a uniform scale of XT, the radiant energy from the three sources lie in entirely different ranges of wave-lengths. The curve shows less than even 1% of the total energy at XT-values below about 1,000 and above 24,000. From low values of XT, the energy rises steeply to a maximum near XT = 3,000 and then falls gently to the higher wave-length side. At the temperature 6,000 K, most of the energy lies in the short-wave part of the spectrum between about 0.17| and 4.0|, with the maximum in the visible part near 0.5|. At 300 K, the energy lies in the long-wave part of the spectrum between about 3| and 80| with a maximum near 10|. At 200 K, the energy shifts further to the long-wave side, with the maximum near 15|. Thus, with decrease of temperature, not only does the wavelength of the maximum emission shift towards the longwave side in accordance with Wien's displacement law, but also the intensity of the short-wave emission decreases.

We, therefore, conclude that radiant energy can be of any wavelength from 0 to infinity depending upon the temperature of the radiating body. Light energy forms only a very small part of it, even less than 3/4th of an octave in the continuous

Light Waves And The Earths Atmosphere

Fig. 6.1 Theoretical curve showing the distribution of black-body radiation at scales of wavelengths, | in microns, corresponding to different temperatures: Scale- A corresponds to T = 6,000K, scale- B to T = 300K and scale- C to T = 200K (Reproduced from Brunt, 1944, © Cambridge University Press,with permission)

spectrum. Saha and Srivastava (1931) in their book on 'A treatise on heat', Fifth edition, reprinted 2003, gives a list of electromagnetic waves discovered so far in the electromagnetic spectrum The range of waves appears to have no limit. The shortest waves discovered so far are the cosmic rays, while on the long-wave side the longest waves are the Hertzian or broadcasting waves. In Table 6.1, we present an extract from this list, showing the broad ranges of electromagnetic waves in the spectrum of radiation.

Table 6.1 Electromagnetic waves in the spectrum of radiation

Name of the wave

Wavelength (|)

Frequency (Hertz)



Cosmic ray

< 10-6

> 3 x 1020

Gamma ray

10-6 -10-4

3 x (1020 - 1018)


10-5 -10-1

3 x (1019 - 1015)


10-2 - 4 x 10-1

3(1 - 1/40) x 1016

Visible light

(4-8) x 10-1

3(1/4-1/8) x 1015


8 x 10-1 - 4 x 102

(3/8) x 1015 - (3/4) x 1012



3 x (1012 - 107)


> 107

< 3 x 107

Table 6.2 Ranges of wavelengths of the electromagnetic spectrum used for different remote sensing techniques


1. Visual photography

2. Multispectral imagery

3. Infrared imagery and spectroscopy

4. Radar imagery, scatterometry and altimetry

5. Passive microwave, radiometry and imagery

Range of wavelengths (|)

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  • elias wood
    What is spectral distribution of radiant energy?
    8 years ago

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