Pictures of the energy density and the energy flow in distributions of incoherent light for various two-dimensional situations are shown and discussed. Rules are introduced that allow one to sketch and to interpret such pictures.
REFERENCES
1.
W. T. Welford and R. Winston, High Collection Nonimaging Optics (Academic, New York, 1989).
2.
P. Würfel, Physik der Solarzellen (Spektrum, Akademischer Verlag, Heidelberg, 2000), p. 34.
3.
H.
Hinterberger
and R.
Winston
, “Efficient light coupler for threshold Cerenkov counters
,” Rev. Sci. Instrum.
37
, 1094
–1095
(1966
).4.
D.
Didascalou
, T. M.
Schäfer
, F.
Weinmann
, and W.
Wiesbeck
, “Ray-density normalization for ray-optical wave propagation modeling in arbitrarily shaped tunnels
,” IEEE Trans. Antennas Propag.
48
, 1316
–1325
(2000
).5.
A. S. Glassner, An Introduction to Ray Tracing (Academic, New York, 1989).
6.
To most of the “radiometric” quantities (energy, energy flow, energy flow density, etc.), a corresponding “photometric” quantity can be defined (quantity of light, luminous flux, illuminance, etc.). The photometric quantities are obtained by multiplying the spectral energetic quantities by a wavelength dependent weighting factor. Thus, all of our energy flow diagrams can also be interpreted as the flow lines of the (photometric) “quantity of light.”
7.
Max Planck, Vorlesungen über die Theorie der Wärmestrahlung (Verlag Johann Ambrosius Barth, Leipzig, 1913), pp. 22–23.
8.
A cosine appears in Eq. (1) when written with the magnitudes of the vector quantities j and See for example, Max Born and Emil Wolf, Principles of Optics (Pergamon, Oxford, 1964), 2nd ed., p. 182, Eq. (5).
9.
In effect we have a six-dimensional phase space with the three space coordinates x, y and z, and three Cartesian momentum coordinates ( and ) equivalent to the spherical bookkeeping (k, ϑ, and φ), where k is the magnitude of the momentum.
10.
Note that the angular resolution cannot be increased arbitrarily, because for the resolution is diffraction limited. (λ is the wavelength of the radiation.)
11.
The radiance meter will indicate the correct value of L only as long as it “sees” the light source under an angle that is greater than its angular resolving power. Thus, if the source is too small and/or too far away, as for example a star other than the sun, the meter will no longer measure correctly.
12.
The energy flow of Eq. (1) can be interpreted as the time average of the Poynting vector. Note, however, that this remark is not of much use. For the kind of fields that we are considering, the distributions of the electric and magnetic field strength are so complicated that there is no possibility to know them and no interest in knowing them. Knowing the electric and magnetic fields of, say, thermal radiation would be a task similar to knowing the positions and momenta of all of the molecules of a material gas in thermodynamic equilibrium.
13.
A free download of LIGHTLAB 2.0 is available at http://www.physikdidaktik.uni-karlsruhe.de.
14.
A.
Wolf
, J.
van Hook
, and E. R.
Weeks
, “Electric field line diagrams don’t work
,” Am. J. Phys.
64
, 714
–724
(1996
).15.
F.
Herrmann
, H.
Hauptmann
, and M.
Suleder
, “Representations of electric and magnetic fields
,” Am. J. Phys.
68
, 171
–174
(2000
).16.
F.
Herrmann
, “Is an energy current energy in motion?
,” Eur. J. Phys.
7
, 198
–204
(1986
).
This content is only available via PDF.
© 2002 American Association of Physics Teachers.
2002
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
