I'm going to expand on the previous answer by saying the Angstrom exponent additionally gives us information about the wavelength dependance of aerosols with regard to light scattering or absorption. The value of this exponent for scattering, the Scattering Angstrom Coefficient, is equal to 4 in the Rayleigh regime (Why is the sky blue?), for example. Attached are a couple of articles that shed light on the subject.
Article Technical Note: Simple analytical relationships between Å ng...
Article Aerosol light absorption and its measurement: A review
The scattering Angstrom exponent ranges from negative values (let's say -1) up to values higher than 2. As Solanki and Florian said lower than 1 exponent indicates predominance of coarse particles.
Values higher than 2 clearly indicate predominance of fine particles (polluted areas or biomass burning).
The absorption Angstrom esponent can be greater than 1 too due to the presence of dust or biomass burning.
what is the Angstrom exponent for the wavelength 500-870 nm. and how do we use it to convert Aeronet 500 nm data to 550 nm and why 550nm data is better than the 500nm data.