Some Electromagnetic Radiation Laws
Electromagnetic waves are transverse waves which consist of electric and magnetic waves with
vibrations at 90 to each other and they travel at a speed of light in vacuum (c  3 108 m / s) . They
can be reflected, refracted, transmitted and can be absorbed by matter. The sun’s energy reaches
the earth through radiation.
Figure from: https://iamchaitanya.files.wordpress.com/2015/07/electromagneticspectrum141b490bac872789434.jpg(Douwloaded on 6/5/2016))
Some basic definitions used study of radiation
Radiometry: It is a science that deals with the measurement of electromagnetic (e/m) radiation
Radiometer: An instrument used for detecting and measuring radiation
Photometry: It is a science that deals with the measurement of visible light
Solid angle (or square radian) () : It is the ratio of area of a surface to the square of the radius
formed from the object to the viewing point (see diagram below). It is a three-dimensional
analogue of angle.
r
A=r2

r
Eye
Figure shows illustration of solid angle () that is defined as ratio of A/r2, where A is area of
shaded surface. The area A doesn’t have to be circular.
The SI unit of solid angle is the Steradian (sr) and is defined as the angle subtended at the viewing
point when r=1 such that =A/r2=1.
Pointance (Radiant flux): This is defined as the power per unit solid angle and is measured in
W(sr)-1. Pointance is very close in meaning to intensity of radiation.
Radiance (sometimes called Sterance): This is the power per unit area per Steradian (sr) and
radiance is measured in Wm-2(sr)-1.
Luminous: This term literally means “light” i.e full of or shedding light and in physics it refers to
light as perceived by the eye.
Candela (cd): This is the basic unit for the measurement of visible light and is defined as:
The intensity of (1/ 683) Wsr 1 of monochromatic radiation of visible light of frequency of
5.4 1014 Hz .
Lumen (lm): It is the SI unit for measurement of luminous (refers to light only) flux and for
isotropic media, 1 lm = 1 cd⋅sr.
Luminance: It is a measure of luminous intensity and is measured in cdm2 .
Spectral energy density (Spectral irradiance) ( B ( ,T)) or ( B ( ,T)) : It is the power of
radiation per Steradian (unit solid angle) per square metre per nanometer (or per Hz) and is
measured in Wsr 1m2 nm1 (or Wsr 1m2 Hz 1 )
Or
Stefan-Boltzmann Law of Radiation
This a law that explains the amount of power radiated from a hot body of area A at thermodynamic
temperature, T. The law is:
P  Ae T 4
Where,
P is the radiated power in Watts (Js-1)
e is the emmsivity and is a measure of how good a body is in radiating radiation:
e=1 for a perfect blackbody
0  e  1 for a graybody
e=0 for a perfect whitebody
A is the surface area of the body
  5.67 108Wm2 K 4 is the Stefan-Boltzmann constant
T is the thermodynamic (absolute) temperature of the body
A blackbody is that which absorbs or emits all radiation falling on it (e=1).
A graybody is that whose emissivity lies between 0 and 1.
A perfect whitebody is that which reflects all radiation falling on it (e=0).
Suppose a body of area, A at a higher temperature T2 is placed in a room at lower temperature, T1 ,
the net power (in W or Js-1) lost by the cold body to the room is:
Pnet  Ae (T24  T14 )
Wien’s Displacement Law of Radiation
Wien’s displacement law is:
 peak .T  2.9 103 mK (both from the same curve)
Where mk means metre-Kelvin and max (wavelength at peak intensity) is the wavelength at
maximum intensity at various temperatures of the intensity versus temperature curves as shown in
the diagram below. This is the wavelength corresponding to the peak of each curve read on x-axis.
Figure from: http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html
Thus  peak  T and this is shown by the red curve in the figure.
Suppose the frequency of radiation corresponding to the peak intensity is f peak ,
Since c  f peak . peak ,
Where c  3 108 m / s , Wien’s law can also be written in frequency form (try to do this).
Rayleigh-Jeans and Max Planck Laws of Radiation
We next look at two prominent scientists who did work on blackbody radiation by plotting graphs
of intensity versus wavelength (or frequency). These scientists were: Rayleigh-Jeans and Max
Planck. From their plots, each came up with a formula for blackbody radiation.
The formula for energy of blackbody radiation per unit volume per wavelength (E) or frequency
(E) according to Rayleigh-Jeans was:
E ( ) 
8
4
T
Or
8 2
E ( ) 
T
3
c
and according to Max Planck,
E ( ) 
8 hc
5
1
.
hc
(e
T
 1)
Or
8 2
E ( )  3
c
h
(e
h
T
 1)
Where  denotes frequency of radiation,  is the Boltzmann constant and h is Planck constant.
If we now plot the energies as a function of wavelength we have the following graph:
Figure shows plot of radiation intensity (not radiation!) versus wavelength (from
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html#c4)
And from the frequency formulae, we can also plot radiation intensity versus wavelength as:
Figure shows plot of radiation intensity versus frequency (from http://hyperphysics.phyastr.gsu.edu/hbase/mod6.html#c4)
Please note:
You can choose to know the formulae in terms of wavelengths or frequencies only for easy of
reading. If your formulae are in terms of wavelengths, you need to have only one graph of intensity
versus wavelength and vice versa (It is not necessary to struggle to know the formulae in the two
forms!)
Interpretation of the graphs.
The Planck equations are the ones which correctly predict blackbody radiation at all wavelengths
or frequencies.
At short wavelengths (or high frequencies), the energy according Rayleigh-Jeans law approaches
infinity and this is not acceptable. This phenomena is called the “Ultraviolet catastrophe”. Try to
see this from the graphs.
At long wavelengths (or low frequencies), both energy curves drop down to close to zero as
expected. This means both formula correctly explain blackbody radiation well but Planck formula
still gives the best curve.
Note that the Planck curve is the one that approximates a bell shape or normal curve.
With best regards.
****End****
Dr Thomas Nyachoti Nyang’onda, Department of Physics, University of Nairobi
6th May, 2016