Introduction:
  Humans are only able to see a minute portion of the electromagnetic spectrum.  LeGrand stated, "Although not completely blind, we are not far from it."  The way in which humans "see" an image is by interpreting the rays of energy that are focused in our eyes. These rays are seen as light, and thus colors and define the object we are looking at.  The power radiated by any thermal source is a function of its temperature.  The range of temperatures present in a thermal source relates directly to the colors visible within the spectrum.  Both Kirchoff and Plank studied the relative characteristics between the visible spectrum and energy radiation.

Kirchoff’s Laws of Spectroscopy state:
    · "A continuous spectrum is emitted by a luminous solid, liquid, or a very dense gas
    · Examples: an incandescent light bulb, glowing coals in the fireplace, element of an electric heater.
    · An emission-line spectrum is emitted by a thin, luminous gas
    · An absorption-line spectrum is produced when white light passes through a cold gas

Planck's Radiation Laws state:
    · The primary law governing radiation is the Planck Radiation Law, which gives the intensity of radiation emitted by a blackbody as a function of wavelength for a fixed temperature.  The Planck law gives a distribution, which peaks at some wavelength.  The peak shifts to shorter wavelengths for higher temperatures, and the area under the curve grows rapidly with increasing temperature.
    · A blackbody is a body that absorbs all the radiation that falls onto it.  It does not reflect any radiation.  It reaches thermal equilibrium with its surroundings, and in thermal equilibrium emits exactly as much radiation it absorbs.  It has emissivity=1.  Emissivity measures the fraction of radiative energy that is absorbed by the body.”

Picture thanks to: http://imagers.gsfc.nasa.gov/ems/visible.html

    The visible spectrum includes all colors that fall within approximately the 200nm to 800 nm range.  The colors included in this range are: white, violet, purple, blue, green, yellow, orange and red.  The concept of a black body refers to the idealized perfect absorber or emitter of radiation which describes the radiation produced as a consequence of thermal activity.  For any black body the temperature T (in degrees Kelvin) is calculated by Planck's radiation law that uses the emittance at a given wavelength (meters).  The following table illustrates the temperatures of various illuminants.
 
 

  One can see from this table, that the range in temperatures is fairly large for various illuminants.  In my experiment I used a tungsten bulb which utilized a variable watt input that determined the intensity of the light.  All of the resultant images produced by the spectrometer are based at a set energy input of approximately 5 watts.  Because of the particular defraction grating in the machine at that time, I was only able to measure wavelengths in the 400-1100 range; thus representing colors from violet to red.

Procedure:
    My experiment was conducted in Shattuck using the SPEX 1000M  Spectrometer.  Results were read through the "Mono1 + V1" single channel Si detector which interprets the intensity of the light as a function of wavelength.  The light source was placed directly in front of the aperture slit, and was leveled to ensure that the intensity was at its greatest value.  The aperture slit width as well as some other parameters were discovered purely on a trial error basis.  Because of the sensitive nature of the spectrometer it was pertinent to make sure all light other than the light source was absent.  Possible light addition could have only come from the computer screen and the natural light that perhaps came in through the cracks in the laboratory doorway.  Scans of the light intensity were taken at several intervals until I obtained a graph that appeared smooth and continuous (this is necessary because the step by step procedure in which the spectrometer operates allows for inaccurate slicing of the recorded data).

    My final  results were reached at when I closed the aperture slit width to 10 micrometers.  When this was done, the graph that was produced showed a very nice curve that represented the varying intensities of light at the various wavelengths between 400-1100nm. (I could only look over a range from 400-1100nm because of the particular defraction grating that was in the apparatus at the time.)   I decided to see how the graphs would compare using two different increment values.  The first set of data was taken using 5.00000 nm increments, while the second set was taken using 1.00000nm increments.  At these settings I was able to accurately show that the varying intensities across the indicated wavelengths.  From this I used Planck's Body Radiation equation to calculate a rough estimate of temperatures at various wavelengths within the selected range.

Results:
    The first graph represents a scan of the light bulb intensity taken with these parameters:

• Scan Start (nm): 400.000
• Scan End (nm): 1100.000
• Increment (nm): 5.00000
• Integration Time (sec): .500000

    The second graph represents a scan of the same bulb but now taken with a smaller increment value  to thus give a more accurate representation of the bulb's intensity.  These were the parameters:

• Scan Start (nm): 400.000
• Scan End (nm): 1100.000
• Increment (nm): 1.00000
• Integration Time (sec): .500000

    One can see from the graphs that the values for the intensity start around .5.  I believe that this is due to the natural background light that perhaps entered the lab room through the cracks in the door frame, or perhaps from the computer screen, thus .5 shall be interpreted as 0 for the start of the graph.  With this in mind, both graphs show a very nice range of intensities within 400-1100 nm. As expected the difference between the two graphs is extremely slight, but was a good contribution to the experiment to ensure accuracy.   From the range of intensities I calculated the approximate temperatures using Planck's black body radiation equation with respect to the range of wavelengths obtained  from the spectrometer.  The results of my calculations stated that the average range of temperatures of the light bulb were approximately between 2,500-3,500 degrees Kelvin.  My calculations proved to be extremely difficult to produce, thus I checked my results (which were not always accurate) with the expected values of different sources.  The following is a chart upon which I evaluated my calculations to make sure that I estimated the appropriate range after calculating a few temperatures:

Picture thanks to: http://micro.magnet.fsu.edu/primer/lightandcolor/colortemp.html

Conclusion:
     This experiment not only allowed me to become acquainted with the operation and analysis of the spectrometer, but it also familiarized me with the relationship between color and temperature.  Through studying Planck's Black Body radiation equation, and applying it to a light bulb, I discovered that I could estimate the approximate range of temperatures found in the bulb by plugging the known wavelength values into Planck's equation.  Though I struggled with the calculations themselves, in the end I was pleased to discover that by comparing my results to known results, my techniques and calculations were accurate.  After performing this lab, I discovered the hidden wonders of the spectrum, and the nature of spectroscopy. I find it extremely interesting that light, a phenomena that we take for granted on a daily basis can be so amazingly complex, and that it contains elements that are truly quite beautiful.   I encourage anyone who has an imagination, to use it, and question the limits of our understanding for, in the famous words of Albert Einstein: