We investigate effects of several-hundred-micron thick luminescence down-shifting (LDS) films composed of sol-gel glass with Zn-based nanoparticles (NPs) dispersed on characteristics of Si solar cells. Their internal quantum efficiencies (IQEs) are successfully measured by separating contributions of downshifted photons in measuring reflectance for 300-400 nm, wavelengths of incident photons absorbed by the NPs. We find that IQEs for this wavelength range are more enhanced by employing thicker LDS films, i.e., LDS films with higher optical densities. We also discuss relationship among the number density of NPs in LDS films, their optical properties, and IQEs of cells. We observe a discrepancy between measured and calculated IQEs and indicate escape of downshifted photons across sides of LDS films as its possible origin.