Fermat?s Principle in the guise of the Principle of least time is illustrated for an object moving from Point A in one homogenous medium to Point B in another. The interface between the media is planar. Several parameters are freely specifiable: a) the speed of the object in each medium. b) the perpendicular distance of Points A and B to the interface. c) the point between the media at which the object traverses the interface.
The simulation shows an object moving from A to B with the parameters specified and you can simultaneously watch a similar object moving from A to B along the path of least time.
If you point the velocity vector off of the colored region, glitches occur that either require you to reload or cause the displayed graphical information to be incorrect.
Identify Major Learning Goals:
Illustrates how Fermat's Principle leads to the bending of trajectories at planar interfaces between two media, thus having an implicit relationship to Snell's Law.
Target Student Population:
Prerequisite Knowledge or Skills:
Basic concepts (such as velocity).
Evaluation and Observation
A good visual demonstration of Fermat's Principle in the context of Snell's Law at an interface between media. This provides a nice introduction to the principle of least time, which should enable calculus level students to understand the derivation of Snell's Law and lead to more in-depth discussions of the topic. It will work well for more conceptually oriented classes as well.
It is very flexible, allowing the user to control the speed in each medium, the thickness of the media, and the point at which the path hits the interface between the media.
The post-text says "we can derive" Snell's Law; however, the connection is not made explicit. No incident or refracted angles are actually measured in the simulation, further making the connection somewhat obscured to the typical first time learner.
As noted in the technical concerns, paths that strike outside of the colored region may have glitches.
Potential Effectiveness as a Teaching Tool
Recommended Use(s) for Material (used for Effectiveness Review): Lecture/Demo
This applet is engaging and interactive.
The "task" and questions associated with the demonstration are not very useful, and are actually a little confounding. The correct answer is actually given every time, so it does not make sense to ask the student to play with it to find the right answer.
General Comments on Effectiveness: It would be nice to have some display of angles, so the connection to Snell's Law would be more explicit.
This would work well as an introduction to the standard problem of deriving Snell's Law from the principle of least time.
Ease of Use for Both Students and Faculty
Intuitive interface gets to the point easily and quickly. No technical support required.
The feedback is reasonable, except that the measurement of "pt" is unclear.