Variational principles play an extremely important role in modern physics. To illustrate the idea, let us look at a simple example from optics involving the reflection and refraction of light at the boundary between two transparent media. What path does the light take in each case? For example, light is emitted from a source s, reflected from a boundary, and detected at a point F. Some possible paths along which the light might propagate to get from S to F are indicated by the dashed lines in Fig. 10.1. Which of these, if any, represents the actual path of the light? We seek an answer by invoking a variational principle known as Fermat’s principle.
KeywordsVariational Principle Geometrical Optic Explicit Function Actual Path Gravitational Potential Energy
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