# 虹的形成可视化 - Rainbow Formation

彩虹形成的交互式模拟，展示水滴中的折射、反射和色散

> 标准页面: https://elysiatools.com/zh/visualizations/rainbow-formation

- **分类:** Physics

## 概述

Interactive rainbow formation visualization demonstrating the optical physics behind one of nature's most beautiful phenomena. Features rainbow physics equations: n₁sin(i) = n₂sin(r) (Snell's law for refraction), D = 180° - 2i + 4r (deviation angle for primary rainbow), D_min ≈ 42° (red light, n≈1.331), D_min ≈ 40° (violet light, n≈1.344). Real-time visualization with two complementary displays: Water Droplet Cross-Section showing the complete light path (incident ray enters from top-left, refracts into droplet at air-water interface, reflects internally at back surface, refracts again at exit point near bottom), and Observed Rainbow Arc showing the classic 40-42° rainbow as seen by observer with ROYGBIV spectrum from outer (red) to inner (violet). Light ray tracing with 7 spectrum colors (Red 700nm n=1.331, Orange 620nm n=1.332, Yellow 580nm n=1.333, Green 530nm n=1.335, Blue 470nm n=1.338, Indigo 420nm n=1.341, Violet 400nm n=1.344). Each color ray traced through the droplet showing different exit angles due to dispersion (violet bends more than red). White incident ray option to show light entering as white beam, spectrum colors option to show separated colored rays exiting droplet. Geometric optics calculation engine solving Snell's law in real-time: given incident angle i (0-90°) and refractive index n (1.0-1.5), calculate refraction angle r = arcsin(sin(i)/n), then deviation angle D = 180° - 2i + 4r. Adjustable parameters: incident angle i (0-90°, optimal ~59° for rainbow), refractive index n (1.0-1.5, water ~1.33, demonstrates how different media affect rainbow formation), droplet radius (50-150 px). Display options: show/hide normal lines (dashed reference lines perpendicular to surface), show angle arcs (visual angle measurement), show ray order (numbered 1-4 for incident, refracted, reflected, exit), animation speed control. Four preset scenarios: Primary Rainbow (standard 59° incidence, n=1.33), Alexander's Dark Band (50° incidence showing the dark region between primary and secondary rainbows), High Dispersion (exaggerated n=1.45 to dramatically show color separation), Custom Angle (45° for exploration). Real-time statistics display: incident angle i, refraction angle r, deviation angle D, and fixed rainbow angles (42° red, 40° violet). Educational content covering three-step rainbow formation process (refraction at entry, internal reflection, refraction at exit), why red appears outside and violet inside (different refractive indices create different exit angles), observation conditions (sun must be behind observer, rainbow centered on antisolar point at 40-42° from sun), secondary rainbow and Alexander's dark band (two internal reflections create fainter outer rainbow at 50-53° with reversed colors), and practical observation tips (lower sun = higher rainbow, best viewing during morning/evening, full circular rainbow visible from elevation). Mathematical foundation includes all four key equations. Multi-language support (zh, en, de, fr, es, ru, pt).

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