The extinction cross-sections of individual, optically confined aerosol particles with radii of a micrometer or less can, in principle, be measured using cavity ring-down spectroscopy (CRDS). However, when the particle radius is comparable in magnitude to the wavelength of light stored in a high-finesse cavity, the phenomenological cross-section retrieved from a CRDS experiment depends on the location of the particle in the intracavity standing wave and differs from the Mie scattering cross-section for plane-wave irradiation. Using an evaporating 1,2,6-hexanetriol particle of initial radius similar to 1.75 mu m confined within the 4.5 mu m diameter core of a Bessel beam, we demonstrate that the scatter in the retrieved extinction efficiency of a single particle is determined by its lateral motion, which spans a few wavelengths of the intracavity standing wave used for CRDS measurements. Fits of experimental measurements to Mie calculations, modified to account for the intracavity standing wave, allow precise retrieval of the refractive index of 1,2,6-hexanetriol particles (with relative humidity, RH < 10%) of 1.47824 +/- 0.00072.