In optics, traditional concave cone lenses used in circular rainbow generation are limited by their significant weight. This study, inspired by the Fresnel lens concept, aims to overcome this limitation. By integrating geometrical optics with Python programming, we accurately controlled the position and angle of serrated structures, transforming the concave cone lens into a lightweight, serrated lens. This innovation achieves a circular rainbow with an inner red and outer purple color arrangement, along with enhanced color vividness. Our design process began with the initial concept of converting a concave cone lens into a serrated lens. To address the suboptimal rainbow effect in the initial design, we proposed an optimization method where multiple serrated edges emit violet light that converges again. We thoroughly analyzed the optical path relationships between adjacent serrations and detailed the manufacturing steps of the serrated lens. To scientifically evaluate the rainbow effect, the projection range of red light on the projection screen was determined by accurately calculating the exit angle of red light. Additionally, two quantitative parameters were innovatively defined: the maximum number of colors at the position of red light and the proportion of the red edge within the rainbow ring. Using TracePro optical simulation software, we validated that, under the same projection distance, the serrated lens produces a more pronounced rainbow projection than conventional concave cone lenses. Our study also explored the effects of different projection screen positions, focal lengths, number of serrations, and central angles on the rainbow effect, offering valuable references for future research and practical applications.

This study presents a controllable method for generating indoor rainbows via water-based triangular prisms by adjusting the curvature of the bottom surface of water-filled rectangular glass aquariums. Bright meter-scale striped rainbows (vertical width: 1.0m, horizontal width: 36.0cm) and large-span arched rainbows (horizontal span: 4.0 m, arch height: 2.0m, spectral vertical width: 36.0cm) are successfully projected. The rainbows originate from solar spectra formed by refraction-reflection-refraction (RRR) processes at air-water interfaces, with their morphologies precisely regulated through geometric optical parameters: striped rainbows exhibit a red-top-violet-bottom distribution, while arched rainbows mimic natural rainbows with red-outer-violet-inner curvature. Based on a ray-tracing model, the quantitative effects of solar altitude angle (α=55°), aquarium inclination angle (θ=2.8°～9.0°), and acrylic glass substrate arch height (h_a=1.5～3.5cm) on rainbow dimensions are systematically revealed. TracePro simulations validate the light intensity distribution and true-color reproduction, showing a maximum irradiance of 1.01 W/m² for arched rainbows under an effective light-entry area of ～9.0cm² at a projection distance of 6.4m. Theoretical predictions suggest that enlarging the aquarium size while optimizing curvature can further enhance brightness to practical application levels. Notably, a counterintuitive optical phenomenon is observed where reversed bending of the acrylic substrate generates upward-arched rainbows, with light from the left side of the curved substrate forming the right side of the arched spectrum. This work provides an innovative solution for visualizing complex dispersion effects in science education and establishes an experimental foundation for architectural optical decoration and artistic projection technologies.