ANALYTICAL CHEMISTRY, VOL. 50, NO. 13. NOVEMBER 1978
parallel plane mirror configuration. The parallel plane configuration boarders on being an unstable cavity resonator, and random optical fluctuations in the cavity can readily reduce the development of lasing in random areas of the beam by causing the rays to scatter or quickly walk out of the cavity. The more selective cavity produces a narrower beam, Figure IC,but the effects of random optical fluctuations become more critical causing larger shot-to-shot energy fluctuations. The dye temperature region corresponding to the generation of the most reproducible mode structure apparently produces a compromise cavity configuration that does not let random optical fluctuations generate too many widely divergent rays, when the thermal lens is too convergent on the one hand, or cause too many random cavity losses when the divergent thermal lens produces a less stable configuration on the other hand. In any case, we have found that careful control of the temperature difference between the dye and the water in the ellipsoidal cavity is necessary to obtain reproducible mode structure. Temperature difference control and knowledge about other experimental conditions that influence the noise level of a laser double beam spectrometer system (21, have
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helped to produce a reliable system for analytical measurements.
ACKNOWLEDGMENT The authors wish to express appreciation to Princeton Applied Research Corp. for their loan of the vidicon system. LITERATURE CITED (1) J. W. Hosch and E. H. Piepmeier, Appl. Specfrosc., Sept./Oct. (1978). (2) J. W. Hosch and E. H. Piepmeier, Appl. Specfrosc., Sept./Oct. (1978). (3) J. M. Drake and R . I. Morse, Opt. Commun., 12, 132 (1974).
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Present address, Los Alamos Scientific Laboratory, P.O. Box 1663, Los Alamos, N.M. 87545.
John R. FitzPatrick' E d w a r d H. Piepmeier* Department of Chemistry Oregon State University Corvallis, Oregon 97331 RECEIVED for review May 4, 1978. Accepted August 14, 1978. This research program was supported by National Science Foundation Grant Number CHE73-05031.
Exchange of Comments on Interferometric Concentration Determination of Dextran after Gel Chromatography Sir: Hagel (1) has described a method to determine the dextran concentration in solution from the relation between its concentration and refractive index. He measures a signal from a Multiref 901 (2) that is presumably proportional to the retardation difference between a dextran solution cell and a reference cell. The signal reading is calibrated against the values of dextran concentration obtained by the anthrone method (3). The method of measuring the refractive index using the principle outlined in the theory presented by Hagel is capable of accurately measuring a small difference in retardations, i.e., less than one wavelength, between the sample and reference cells. Therefore, it is a very good method for determining a small refractive index such as that of a gas. Likewise, it is suitable for the detection of very small concentration differences between solutions. However this method is not capable of determining the order of the retardation differences. If one dextran solution produces a retardation difference of a fraction of one wavelength and another produces an equal retardation plus a number of whole wavelengths, the Multiref 901 reads the same signal. Therefore, the retardation difference between the sample and reference cells, and hence the refractive index of the sample, cannot be unambiguously determined unless the order is known. Hagel did not offer a solution to resolve this ambiguity. This note is written to point out that erratic results may be obtained unless this matter is resolved, and also to offer the solution. Fortunately there are ways to determine the order of retardation difference. The use of a compensator with white light can determine the order and may resolve this problem. The number of orders contained in the retardation difference can also be determined by measuring the retardation
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a t two wavelengths that are slightly different ( 4 ) . The magnitudes of the measured retardation difference can be used to calculate the number of orders. Suppose that the number of orders contained in a retardation difference is n, the additional fraction of retardation is AI when using light with wavelength AI, and for light with wavelength A*. The path difference of the light between the sample and reference cells is the same for the two wavelengths, provided that the wavelengths are close enough to neglect the effect of dispersion. Therefore,
( n + l J X 1 = ( n + A,)& From this it can be shown that
(1)
Thus, the retardation difference can be readily determined as ( n + 1 ) A .
LITERATURE CITED (1) Lars Hagel, Anal. Chem., 50, 569 (1978). (2) "Multiref 901, Instruction Manual", Optilab AB, Box 138, S162 12 Vallingby 1, Sweden. (3) J. R. Burt, Anal. Blochem., 9, 293 (1964). (4) F. El-Hosseiny, J . Opf.SOC.A m . , 65, 1279 (1975)
F. El-Hosseiny* R. D. Gilbert Fiber Sciences Department Weyerhaeuser Company 3400 - 13th Avenue S W Seattle, Washington 98134 RECEIVED for review May 19, 1978. Accepted August 7, 1978.
Q 1978 American Chemical Society
