Analytical study and experimental demonstration of light refraction in one-dimensional gradient-index media

Light propagation in gradient-index media has commonly been investigated using specialized optical setups and advanced mathematical formalisms, limiting its accessibility in high school physics education. Therefore, this research investigates the light trajectory in a varying refractive-index medium using basic laboratory equipment, with an emphasis on describing the light path through accessible high-school-level mathematics grounded in Snell’s law. Experimentally, the gradient-index medium was approximated using an eight-layer structure of aqueous propylene glycol solutions with concentrations from 0 to 70 percent by volume in increments of 10 percent. Each layer had a thickness of 2.5 cm, resulting in a variation in refractive index along the vertical direction. A laser beam with a wavelength of 532 nm was directed through the medium, and the resulting light path was recorded using a camera positioned perpendicular to the setup. Coordinate data of the light trajectory were extracted from the recorded images and compared with theoretical predictions. The analysis showed that the light trajectory can first be expressed in a general integral form depending on the refractive-index distribution of the medium. In this case, the refractive index varied linearly with position, and a closed-form analytical solution for the light trajectory can be derived as an inverse hyperbolic function. The experimental results showed trends consistent with the theoretical model. This study demonstrates that light refraction in varying media can be explained through accessible concepts without requiring advanced mathematics. This approach can also be applied in optical demonstrations and the study of light behavior in real physical environments.