Abstract
Abstract
The refractive index is a fundamental optical parameter that governs the interaction of electromagnetic radiation with transparent dielectric media, determining the extent of refraction, reflection, and transmission at material interfaces. In this work, we present a straightforward, non-interferometric method for the accurate determination of the refractive index of plane-parallel dielectric slabs and thin polymer blend films based solely on measurements of normal-incidence laser transmittance. By exploiting the incoherent (thick-sample) limit of the Fabry--P\'{e}rot transmission formula, the refractive index is expressed as a closed-form analytic function of the measured transmittance, thereby eliminating the need for phase-sensitive or interferometric instrumentation. We further extend the formalism to include the effect of residual absorption through the Beer--Lambert factor, and complement the intensity-based measurement with a Mach--Zehnder interferometric scheme that provides full-field optical path difference maps, from which spatially resolved thickness distributions are retrieved. The method is validated on two distinct classes of samples. First, five bulk optical-grade dielectric slabs---borosilicate glass, BK7 optical glass, fused silica, PMMA, and polycarbonate---are characterised, yielding refractive indices in agreement with reference values to within $|\Delta n| \lesssim 5\times10^{-3}$ for polished glasses, together with full-field thickness maps of sub-100~nm RMS accuracy and an independent rotation-based fringe-counting cross-check. Second, the technique is applied to a series of polyvinyl alcohol--polyvinylpyrrolidone (PVA--PVP) polymer blend thin films spanning the full composition range, for which the effective refractive index is found to decrease monotonically from $n_{\text{eff}} = 1.724$ (pure PVP) to $n_{\text{eff}} = 1.534$ (pure PVA), in excellent agreement with the Lorentz--Lorenz effective-medium model, from which the intrinsic indices of the constituent polymers are extracted as $n_{\text{PVA}} = 1.536$ and $n_{\text{PVP}} = 1.724$. Across both sample classes the method achieves an estimated uncertainty of $\delta n \approx 0.003$ for a transmittance measurement precision of $0.5\%$, comparable to standard Abbe refractometry, establishing the transmittance-based approach as a versatile, low-cost, and non-destructive optical metrology platform applicable to any optically homogeneous, weakly absorbing dielectric slab or film.