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Unformatted text preview: c_Absorption_Bands_png. emit at 10.6µm. From this graph, determine the center frequency ω0 and linewidth γ (measured full
width at halfmaximum) of the CO2 absorption peak.
1 Mauna Loa has written about their measure procedure and mean measurements (since 1958!) at http://www.esrl.noaa.
gov/gmd/ccgg/trends/co2_data_mlo.html. 1 6.007 Spring 2011 Problem Set 7 4. What is the peak absorption coeﬃcient at this absorption line? Compare this to the absorption line
measured for 350ppm.
5. If a 1mW beam at 10.6µm wavelength hits CO2 , what is the output power after traveling 10m?
6. Will the absorption coeﬃcient measured in an experiment be smaller or larger than the calculated
value? Why? Problem 7.2, Two Slit Spectrometer
Following the results of the previous problem, you would like to make a measurement of the concentration of
the carbon dioxide in the air. To do this we would like to look at the absorption of the air across the range
of wavelengths carbon dioxide has some absorption. You could try measuring the absorption at individual
wavelengths with discrete detectors and sources, but it would be faster if you could make one measurement
at several wavelengths at the same time. To make the measurement in one shot you use something called
a spectrometer. In this problem we will look at a spectrometer based on the two slit grating discussed in
class. (a) Using theory from the two slit interference pattern shown in class, ﬁnd the angle of the ﬁrst oﬀ axis
interference maximum (ﬁrst order fringe) as a function of slit distance and wavelength. Assume the
width of the slits is negligible.
(b) If we are interested in the wavelength region from 9 − 11µm how far away from the slits would we
need to place our camera so that this wavelength band is spread over 1 cm. Assume that the slits are
separated by d = 50µm and that we want the 10µm wavelength to occur in the center of the pattern.
(c) How does the interference pattern change as we increase the number of slits?
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This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.007 at MIT.
 Spring '11
 VladimirBulovic
 Electromagnet

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