Absolute Determination of Refractive Indices of Gases at 47.7 Gigahertz

Abstract

The refractive index of a gas is determined to high accuracy by measuring the change in the resonant frequency when the gas is admitted to a previously evacuated microwave cavity. This measurement was made at a frequency of 47.736 GHz, and is the first such measurement in this frequency range. The resonant frequency of the cavity is detected by means of a hybrid tee bridge circuit. When the cavity is matched to the waveguide the null at resonance is very sharp, and the frequency can be set to ±5 parts in 10⁸. Two types of resonant structures were used in this measurement, a conventional cylindrical cavity and a Fabry‐Perot resonator using one plane and one spherical mirror. Measurements were made with both structures on each of the gases, and the agreement between the two was within the limits of experimental error. Because the Fabry‐Perot resonator has no side walls, air could be passed through it much more easily, and it is therefore preferred for use with moist air. The values of (n−1)×10⁶ for the gases at 0°C and 760 Torr are as follows: $$\begin{array}{cc}{\mathrm{Dry\; CO}}_2\hspace{0.17em}\mathrm{free\; air}& \text{288.13±0.05,}\\ \mathrm{Argon}& \text{277.48±0.05,}\\ \mathrm{Carbon\; dioxide}& \text{495.16±0.08,}\\ \mathrm{Helium}& \text{34.51±0.05,}\\ \mathrm{Hydrogen}& \text{135.77±0.05,}\\ \mathrm{Nitrogen}& \text{293.81±0.07,}\\ \mathrm{Oxygen}& \text{266.95±0.05.}\end{array}$$ The primary values of these results lies in their increased accuracy over previous measurements and their confirmation of existing accurate data on these gases. In addition the use of the Fabry‐Perot resonator as a refractometer is demonstrated and its advantages under certain conditions discussed.