When a ray of light passes through an optical instrument, such as a telescope or a photographic lens, it undergoes a change of direction as it strikes each refractive or reflective surface. We can describe the path of the light ray once we know the two simple laws which govern the change of direction. One of these is the law of refraction which was discovered by Snell about three hundred years ago; and the other is the law of reflection, which was known to Archimedes nearly two thousand years before. Figure i gives a simple example of a ray, A—B, passing through two lenses and undergoing a change of direction at each of the four surfaces in accordance with Snell’s law. From a much more general point of view, Fermat summed up the whole career of a light ray. In passing through media of varying optical densities light is propagated at correspondingly varying speeds, and the path which it follows is such as would have to be chosen by the light if it had the purpose of arriving within the quickest possible time at the destination which it actually reaches. (Here it may be remarked, in parenthesis, that any two points along the path of the light ray can be chosen as the points of departure and arrival respectively.)
当光线穿过如望远镜或照相透镜等光学仪器时，其照射到每个折射或反射面上，传播方向便都会发生改变。一旦我们知道了控制光线方向变化的两个简单定律，就可以描述它的路径，其中一个是折射定律，大约300年前由斯涅尔（Snell）发现；另一个是反射定律，阿基米德早在两千年前就已知晓。图1给出了一个简单的例子，一条光线A-B，穿过两个透镜，根据斯涅尔定律（Snell’s law），在四个表面中的每一个表面上都会发生传播方向的改变。从更为普遍的观点来看，费马（Fermat）总结了光线传播的整个变化过程。在通过不同光密度的介质时，光以相应的不同速度传播，而它所遵循的路径，也是光线传播的必然选择，是使它能够在最短的时间内到达实际的目的地（这里要在括号中指出的是，沿着光线路径上的任意两点都可以分别作为出发点和终点）。任何偏离射线实际选择的路径都意味着延迟，这就是著名的费马光学最小时间原理。它通过非常简洁的陈述，定义了光的整个传播过程，当然也包括了更普遍的情况，即介质的性质不会突然改变，而是从一个点到一个点逐渐变化，地球周围的大气就是这样的例子。
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