Analysis of optical pattern formation on glass: exploring light phenomena in the International Physicists Tournament

TL;DR

This paper addresses how random scratches on glass produce optical halos and related pattern distortions, explicated through a geometric-optics framework validated by Defocusing Microscopy of scratch topography. It combines experiments with polished and scratched plates, a Python-based simulation of ray reflection, and specular holography to engineer square and circle patterns, demonstrating both explanatory power and pattern-design potential. The key findings show halos arise from specular reflections at surface irregularities, with halo density modulated by scratch count and the light–camera geometry, and that the model accurately reproduces observed halos and distortions. Practically, the work offers an accessible educational approach for teaching geometric optics, and provides a computational tool to explore optical pattern formation on everyday reflective surfaces.

Abstract

Motivated by a problem from the 2023 International Physicists' Tournament, we investigate the formation of particular patterns when light passes through glass. Experimentally, we use various glass plates, registering each reflected and transmitted outcome. Thus, we find the condition to form a common pattern, namely, randomly scratched plates produce the halos. We engineer other optical patterns by means of the specular holography method. Using the Defocusing Microscopy technique, we study the geometric properties of the glass, establishing the physical and mathematical model for a simulation. Our computational results agree well with the experimental ones, leading us to conclude that the pattern formation is governed by specular reflection on various points along the scratches. Our findings give an initial explanation for the pattern formation on glass, in particular for the halo design. We also show that the IPT open questions help students learn physics concepts and develop research skills.

Figures (14)

• Figure 1: Halo pattern seen on (a) a spoon, (b) a car surface and (c) a ruler.
• Figure 2: (a) Experimental setup. Inset: Sketch showing the important parameters. For illustrative purposes only. (b) Glass plates described in Table \ref{['Table 1']}. Since light is not hitting the glass surface perpendicularly (it is coming from above), we do not see the formation of optical patterns here.
• Figure 3: Simulation outline. The plane containing the light source and the detector is parallel to the plate, as seen in Fig. \ref{['Fig. 1']}; here the image is rotated to visualize better. The incoming ray reaches the scratch and is reflected towards the camera. The reflection is seen (plotted) if it obeys the tolerance criterion.
• Figure 4: Schematic figure of the drawing process. One leg of the compass stays on the blueprint, following the points along the desired shape.
• Figure 5: Halo formation for plates scratched with (a) a coarse grit, (b) with a medium grit and (c) with a fine grit.