Radiant Power and Action Spectra
1) Data for the spectral power distribution function, of a source is very closely approximated by
5000 (1 600)2
Where the result is in watts/nm, and the wavelength A. is in nm.
a) Plot this spectral power distribution between 200 nm <). < 1000 nm. Take care to properly label this
b) What is the total number of watts emitted by the source in the wavelength band a < 2000 nm? Use
Calculus and your head, Mathematica/MATLAB/MathCAD, or an approximating sum on a
c) What is the total number of watts emitted by the source in the visible wavelength band,
400 nm <% 700 nm?
d) Where does this SPD function attain its maximum value?
2) Most naturally occurring sources of light are objects that give off radiant power because they are heated to
incandescence. Early man-made electric light sources used this same principle. A modem example is the
incandescent lamp in your living room. Many incandescent lamps have a tungsten wire heated electrically to
a temperature of approximately 2850 K, at this temperature an incandescent wire emits "light.
Recall from your elementary physics that Planck's Law predicts the power emitted by a so-called blackbody
radiator as a function of wavelength. Real incandescent objects have approximately 1/2 the emitting power of
true blackbody radiators. So, an object that is incandescent has a spectral power distribution function that
can be obtained from Planck's Law:
d.2(1) m-2 = 0.5
Where C1 = 3.7415 x 10 16 W m² C2 = 1.43878 x 102 K m, and T = temperature in Kelvins
a) Note the left hand side of the equation. Describe what the right hand side evidently gives us.
b) Perform a units analysis on the equation given above, showing the final units are: Wm) -2
c) What must be the units of wavelength, a in this equation?
d) Using wavelength increments no smaller than 10 nm, plot the spectral power distribution functions for
an object with surface area of 0 .08 m° and that exhibit temperatures of 2800 K, 3500 K, 4000K, and
10,000 K. Use the wavelength range of 300 nm to 2000 nm. (You will need at least two plots)
e) Assume that the object has 0.20 cm² of surface at a temperature of 2900K.
Plot the spectral power distribution function for this radiator. Use the wavelength range of
380 nm to 750 nm.
What are the total number of radiant watts produced by this object between the wavelengths
of 380 nm and 750 nm?
f) The 100 W incandescent lamp in your living room converts electrical power into radiant power with an
efficiency of very nearly 100%. It puts 10% of this radiant power into the visible region of the
spectrum (400 nm nm). What must be the total surface area of the ncandescent tungsten
wire? (remember, from above, the temperature of the tungsten wire is approximately 2850 K.)
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