3 Simulations designed to help students understand the Principle of Least Action.
- Enable students to verify or derive
$\theta_i = \theta_r$ - Give students an insight into the optimization proof that results in Reflection
- Clarify misconceptions (i.e., equal angles means incident ray hits metal equidistant from both points)
- Help students verify or derive
$n_1\sin\theta_1 = n_2\sin\theta_2$ - Give students an insight into the optimization proof that results in Refraction
- Clarify student questions (i.e., Why don't straight paths minimize time? What about paths that minimize the distance taken in water?)
- Give students an insight into the tug-of-war between the two parameters of path length and acceleration that determine the path of least time.
- Demonstrate how the principle of least action analytically determines the path of least time in the Brachistochrone problem.
- Aid students in drawing the analogy between the Brachistochrone problem and the behavior of light. In fact, Johann Bernoulli's solution to the problem was to imagine the brachistochrone as a path of light traveling through an optically homogenous medium.
You will find 3 Jupyter Notebooks, each containing step-by-step instructions explaining how to use each of the three simulations of the LAP in Optics.