Ben-Benjamin Jonathan S, Cohen Leon
Department of Physics, Hunter College and Graduate Center, City University of New York, New York, New York 10065
J Acoust Soc Am. 2015 Feb;137(2):EL171-7. doi: 10.1121/1.4905879.
The equations of motion for a ray in a Snell's law medium with a varying index of refraction are derived. A stratified medium is considered. Explicit expressions are given for the velocity and acceleration components of the ray. These are derived directly from Snell's law. It is further shown that the propagation of a ray can be modeled in terms of Newtonian-like equations of motion and that momentum is conserved along the interface. It is shown that Snell's law follows from this conservation law. Properties of the motion are studied and an example is given.
推导了光线在折射率变化的斯涅尔定律介质中的运动方程。考虑了分层介质。给出了光线速度和加速度分量的显式表达式。这些表达式直接由斯涅尔定律推导得出。进一步表明，光线的传播可以用类似牛顿运动方程来建模，并且动量在界面处守恒。结果表明，斯涅尔定律可由该守恒定律推导得出。研究了运动的性质并给出了一个例子。
