GENERATING CIRCULAR RAINBOWS THROUGH THINNING CONCAVE CONICAL LENS WITH THE PRINCIPLE OF FRESNEL LENS

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.