  Absorption and scattering properties of nanoparticles immersed in an
absorbing medium are essential in understanding the overall properties of
composites and in designing materials with expected functionalities. In this
paper, we establish the model that links the absorption and scattering
coefficients of individual particles with the reflectance and transmittance
spectra of thin-film composite, supported by well-controlled experiments. Thin
films consisting of TiO$_2$ nanoparticles embedded in PMMA are fabricated on
glass substrates using spin-coating and then peeled off to form standalone
samples for spectroscopy measurements. The absorption $K$ and scattering $S$
coefficients of multiple nanoparticles are calculated from the measured
transmittance and reflectance using the Kubelka-Munk theory in combination with
the Saunderson correction. From the theoretical side, the absorption $K$ and
scattering $S$ coefficients are the accumulation of absorption and scattering
of individual particles, which are derived from the Mie theory. The agreement
between the $K$ and $S$ coefficients extracted from experimental data and from
theoretical calculations gives deep insight into the significant attenuating
effect of absorption and scattering on each particle due to the surrounding
medium. Furthermore, the validated model of nanoparticles immersed in an
absorbing medium can be used to obtain the preliminary results for materials
designed toward radiative cooling.
