Single-particle trapping is an effective strategy to explore the physical and optical properties of aerosol with high precision. Laser-based methods are commonly used to probe the size, optical properties, and composition of nonlight-absorbing droplets in optical and electrodynamic traps. However, these methods cannot be applied to droplets containing photoactive chromophores, and thus, single-particle methods have been restricted to only a subset of atmospherically relevant particle compositions. In this work, we explore the application of a broadband light scattering approach, Mie resonance spectroscopy, to simultaneously probe the size and the refractive index (RI) of droplets in a linear quadrupole electrodynamic balance. We examine the evaporation of poly(ethylene glycol)s and compare the calculated vapor pressures with literature values to benchmark the size accuracy without prior constraint on the RI. We then explore the hygroscopic growth and deliquescence of sodium chloride droplets, measuring RI at the deliquescence relative humidity and demonstrating agreement to literature values. These data allow the wavelength dependence of the RI of aqueous NaCl to be determined using a first-order Cauchy equation, and we effectively reproduce literature data from multiple techniques. We finally discuss measurements from a light-absorbing aqueous droplet containing humic acid and interpret the spectra via the imaginary component of the RI. The approach described here allows the radius of nonabsorbing droplets to be determined within 0.1%, the refractive index within 0.2%, and the first-order term in the Cauchy dispersion equation within similar to 5%.