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Curving the Trajectory of Light in Refraction Index Gradients

Oliver Polachini, Fabricio Marques

TL;DR

This work investigates how refractive-index gradients bend light and create mirage-like distortions. By developing a theoretical framework with a linear gradient $n(y)=n_0 - k y$ and solving for the trajectory, the authors connect boundary conditions to observable paths, then validate the model with two gradient schemes. A 51-layer sugar concentration gradient enables measurable ray bending and successful image reconstruction, while a temperature gradient proves less effective in this setup; wavelength effects are found to be negligible within experimental uncertainty. The study showcases an accessible, high-school–level approach to gradient-index optics and demonstrates how active-learning experiments can yield quantitatively consistent image reconstructions, with potential for curricular integration and further exploration of gradient phenomena.

Abstract

This work seeks to present an investigation about the trajectories followed by rays of light passing through refractive index gradients that was entirely carried by high school students. Such trajectories are curved, therefore contradicting the common sense that light should always travel along straight lines. This fact causes the formation of distorted and striated images, similarly to a type of mirage known as Fata Morgana. Using a rectangular aquarium containing solutions with different gradients of sugar or water with a temperature gradient, we analyzed the conditions for image inversion to occur. Also, we were able to reconstruct a distorted image through our theoretical predictions.

Curving the Trajectory of Light in Refraction Index Gradients

TL;DR

This work investigates how refractive-index gradients bend light and create mirage-like distortions. By developing a theoretical framework with a linear gradient and solving for the trajectory, the authors connect boundary conditions to observable paths, then validate the model with two gradient schemes. A 51-layer sugar concentration gradient enables measurable ray bending and successful image reconstruction, while a temperature gradient proves less effective in this setup; wavelength effects are found to be negligible within experimental uncertainty. The study showcases an accessible, high-school–level approach to gradient-index optics and demonstrates how active-learning experiments can yield quantitatively consistent image reconstructions, with potential for curricular integration and further exploration of gradient phenomena.

Abstract

This work seeks to present an investigation about the trajectories followed by rays of light passing through refractive index gradients that was entirely carried by high school students. Such trajectories are curved, therefore contradicting the common sense that light should always travel along straight lines. This fact causes the formation of distorted and striated images, similarly to a type of mirage known as Fata Morgana. Using a rectangular aquarium containing solutions with different gradients of sugar or water with a temperature gradient, we analyzed the conditions for image inversion to occur. Also, we were able to reconstruct a distorted image through our theoretical predictions.

Paper Structure

This paper contains 11 sections, 18 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Foundations
  3. Formation of Mirages in Nature
  4. Trajectories of Light Rays
  5. Experimental Procedure
  6. Temperature Gradient
  7. Gradient of Sugar Solution at Different Concentrations
  8. Experimental Analysis
  9. Reconstruction of Images
  10. Conclusions
  11. Influence of the Wavelength

Figures (13)

  • Figure 1: Comparison between the standard atmospheric configuration and the situation for which the Fata Morgana mirage occurs.
  • Figure 2: Graphic representation of curved paths followed by light causing a Fata Morgana mirage.
  • Figure 3: Graphic representation of the aquarium used in the experiments.
  • Figure 4: Geometry of the transition of a light ray from layer $i$ to $i+1$.
  • Figure 5: Apparatus consisting of (a) an aquarium where a gradient of temperature was produced and (b) lasers of different frequencies/wavelenghts.
  • ...and 8 more figures