In this problem we examine experimental absorption spectroscopy data. The output of a vari...

In this problem we examine experimental absorption spectroscopy data. The output of a variable-frequency diode laser is divided at a beam splitter so that part of the laser beam is incident on a Fabry-Perot cavity of fixed length and part of the laser beam passes through a sample cell containing atmospheric oxygen, as shown in Figure 1a. An overlay of the scaled transmittance through the Fabry- Perot cavity (solid curve) and the scaled transmittance through the oxygen cell (curve made with + symbols) as functions of the laser frequency change is shown in Figure 1b. The dips in the transmittance through the oxygen cell indicate that the oxygen molecule strongly absorbs these frequencies. The free spectral range of the Fabry-Perot cavity used in the experiment was known to be 11.6 GHz. The free spectral range can be taken to be the distance between the tall transmittance peaks, indicated by the arrows in Figure 1b. (A spherical-mirror Fabry-Perot cavity was used in the experiment and so the transmittance includes peaks corresponding to both longitudinal and transverse modes.)

a. Estimate the difference in the frequencies of the two absorption dips shown in Figure 1b.

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b. Estimate the “full-width-at-half-depth” of each absorption dip.

Figure 1 (a) Experimental arrangement, (b) Overlay of transmit- tancc curves. (Courtesy of R. J. Brecha, Physics Department, University of Dayton.)