In Section A , we noted that the speed of sound in air depended on both the molecular weight and the temperature of the air. We also noted that the speed of light depended on both the electrical permittivity and the magnetic permeability of the medium. It is a general characteristic of waves that their phase velocity depends on the medium in which they travel . While we will shift our attention to light, we note that everything we will be discussing still applies to other types of waves. We have seen that particles in a potential field will move to the position of least energy and that electricity takes the path of least resistance .
Waves are no different.
They follow the path of least total elapsed time. The action is defined as the integral of the difference between kinetic and potential energy with respect to time. Everything in nature behaves the way it does because it follows the path of least action . Another of nature's deepest mysteries is why this must be so. The index of refraction is the ratio of the phase velocity in a standard medium, ie.