A reciprocal-magnification regression liquid-lens method for refractive-index measurement

A reciprocal-magnification regression liquid-lens method is presented for determining the refractive index of transparent liquids. In this approach a fixed vertical plano-convex lens is provided by a thin-walled transparent vessel filled with liquid. A standard ruler was used to measure the object position s along a fixed vertical reference scale. The reciprocal magnification is defined as the inverse of the measured transverse-magnification magnitude. Linear regression of object position against this quantity gives the focal length from the fitted slope, while the unknown effective reference-plane position is absorbed into the intercept. The refractive index is then obtained from the measured vessel curvature and the fitted focal length, without requiring direct localisation of the principal plane or focal point. Using the vessel's radius of curvature $R = 13.72$ cm in this study, the method gave f = 41.73±0.30 cm and n = 1.329±0.003 for water, and f = 34.31±0.25 cm and n = 1.400±0.003 for a 40% (w/w) sucrose solution. The reliability of the results was supported by calibrating with a standard lens and performing two independent liquid-lens consistency checks. These partial propagated standard uncertainties include contribution from the regression fit, vessel curvature and common object-size reading, the latter evaluated using an assumed rectangular distribution; they exclude unquantified optical-model effects. The method is simple, graphical and suitable for undergraduate optics experiments.