Measurements of optical properties of liquids in a quartz cuvette: Rigorous model, uncertainty analysis and comparison with popular approximations

Authors:

• Jarosław Judek,
• Konrad Wilczyński,
• Jerzy Piotrowski

Abstract

In this paper we construct and comprehensively analyze the strict optical model of a quartz cuvette filled with investigated liquid, that is typically used in spectrophotometry measurements. We do not make any assumptions concerning the scale of reflections or attenuations but we assume no scattering. We perform uncertainty analysis assuming uncertainties of transmittance and reflectance close to those met in our experiments. Neglection of the reflectance, which is typical for popular approximations, makes the calculation of the real part of the liquid refractive index impossible and introduces systematic errors to the calculations of the absorption coefficient. Therefore, we calculate values of these systematic errors and we compare them to the uncertainties. This allows us to determine the accuracy of popular approximations, particularly, we demonstrate that an approximation in which the transmittance is normalized to the transmittance of a cuvette filled with pure non-absorbing solvent is valid.