Normal-incidence specular transmittance of undoped amorphous selenium (a-Se) films of several thicknesses ( 0.25 1 μm ) thermally evaporated on thick microscopic glass-slide substrates upheld at temperatures near 30 (below glass transition temperature of undoped Se) has been measured at room temperature in the spectral wavelength range 300 1100 nm. Above a threshold wavelength (~ 600 nm), their as-measured curves display transmittance values near that of glass substrates and exhibit well-resolved interference-fringe maxima and minima, signifying good uniformity of fabricated a-Se films. Below , the curves decline progressively to zero transmittance, preceded by a tailing-like trend of possible structural disorder origin. The spectral dependencies of optical constants and of the studied a-Se films on were retrieved from iterative curve-fitting of their -data to theoretical -formulations of an air-supported {thin film/thick substrate}-stack using the O'Leary-Johnson-Lim (OJL) interband-transition dielectric model, combined with a dielectric constant , representing the dielectric background at very high photon energies (at spectral wavelengths much smaller than measured). Regardless of the number of observed interference fringes, reliable simulation to the as-measured normal-incidence -spectra has been achieved, but were remarkably curve-fitted if we presume that a thin roughness layer ( 5 nm) of selenium was formed on top of the fabricated undoped a-Se films. The retrieved spectra display a broad peak around ≅ 0.52 μm, below which was found to vary with wavelength in accordance with a Sellmeier-like (Wemple-DiDominco) single-oscillator (normal) dispersion formula, with a static index of refraction 0 ≅ 2.42, where is the static dielectric constant of the material at zero photon energy , and an oscillator "average" bandgap energy of ≅ 3.93 eV ≅ 2 , the optical (Tauc) bandgap energy. The values of of studied undoped a-Se films deduced from Tauc-like plots were around 1.92 eV ( 0.02 eV) and the retrieved values of OJL band-tailing energy parameter (Urbach-tail parameter Γ ) was found to be in the range 40 50 meV, slightly dependent on film thickness.