Using refractive index gradients to measure diffusivity between liquids

One most commonly thinks of refraction occurring when light strikes at an angle to an interface separating two regions with different refractive indices. However, a light ray traveling normal to such an interface will also be refracted, if the second region has a refractive index gradient parallel to the interface plane. If liquid–liquid interdiffusion produces such a gradient in the second region, then one can infer the diffusivity of solute particles by measuring the time-dependent refraction. We have performed such diffusion experiments with three different aqueous solutions and found reasonably good agreement with diffusivity values given in the literature. The experimental setup and data analysis are simple enough for an undergraduate student to complete in a few weeks, making this investigation ideal for inclusion in an advanced laboratory course.