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通过对一道以光的色散为背景知识的高考题的解读,分析了彩虹形成的物理过程,说明了彩虹的形成与光通过三棱镜色散的物理过程之间的区别。介绍了笛卡尔光线以及最小偏向角;从数学的角度解释了彩虹形成的原因;利用微分的知识准确地计算出了彩虹形成时光线的折返角,并由此进一步解释了彩虹的颜色分布和形状。
Through the interpretation of a college entrance examination with the background of light dispersion, the paper analyzes the physical process of rainbow formation and shows the difference between the formation of rainbow and the physical process of light dispersion through prism. Introduced the Cartesian light and the minimum deflection angle; explained the reason of the rainbow formation mathematically; used the knowledge of differential to accurately calculate the turn-back angle of the light when the rainbow was formed, and further explained the rainbow’s color distribution and shape .