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单词 Principle of stationary time
释义

Principle of stationary time

中文百科

费马原理 Fermat's principle

(重定向自Principle of stationary time)
皮埃尔·德·费马
光线从点Q传播至点O时,会被半圆形或混合形镜子反射,最终抵达点P。
光线从点Q传播至点O时,会被混合形状镜子反射,最终抵达点P。
光在平面上的反射

费马原理(Fermat principle)最早由法国科学家皮埃尔·德·费马在1662年提出:光传播的路径是光程取极值的路径。这个极值可能是最大值、最小值,甚至是函数的拐点。 最初提出时,又名「最短时间原理」:光线传播的路径是需时最少的路径。

费马原理更正确的称谓应是「平稳时间原理」:光沿着所需时间为平稳的路径传播。所谓的平稳是数学上的微分概念,可以理解为一阶导数为零,它可以是极大值、极小值甚至是拐点。

费马原理是几何光学的基本定理。用微分或变分法可以从费马原理导出以下三个几何光学定律:

最短光时线可以有多条,例如光线从椭圆面焦点A经过反射到另一焦点B,可以有无数条路径,所有这些路径的光线传播时间都相等。

英语百科

Fermat's principle 费马原理

(重定向自Principle of stationary time)
Fermat's principle leads to Snell's law; when the sines of the angles in the different media are in the same proportion as the propagation velocities, the time to get from P to Q is minimized.
Pierre de Fermat
皮埃尔·德·费马
光线从点Q传播至点O时,会被半圆形或混合形镜子反射,最终抵达点P。

In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light. However, this version of the principle is not general; a more modern statement of the principle is that rays of light traverse the path of stationary optical length with respect to variations of the path. In other words, a ray of light prefers the path such that there are other paths, arbitrarily nearby on either side, along which the ray would take almost exactly the same time to traverse.

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更新时间:2025/6/18 9:26:23