The teaching of optical phenomena can be enhanced through the use of analogies to the motion of a bi-frequency pendulum. In this text we target demonstrations to four groups of students and scientists: younger schoolchildren to high school seniors, 7th graders to college juniors; college juniors to final-year graduate students in physics, optics and engineering; and college seniors to research scientists. The main difference between the groups is in the level of mathematics required to make the analogy to optical phenomena. Most of the physical ideas may be understood and appreciated even in junior high school and serve as a motivation for deeper study of mathematics and science.
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