Location:

SS Ballroom DE 
Date:

Wednesday, Aug.3 
Time:

8:00 AM 8:10 AM

Author:

David Schuster, Western Michigan University
269 3875844, david.schuster@wmich.edu

CoAuthor(s):

Betty Adams , Adriana Undreiu

Abstract:

Investigating and discovering a law for refraction is potentially an ideal activity for inquirybased physics. However, the law of refraction involves sine functions; this complicates an empirical search for a law (as it did historically) and may also seem to preclude it for students with no trigonometry. Wanting a guideddiscovery approach nonetheless, we "invented" a geometrical representation: incident and refracted ray directions can be specified not only by angle but by semichords in a reference circle. This proves very successful: students discover that various possible relationships, such as angle ratios, are initially promising but do not work at large angles; and they finally arrive at a simple and visually elegant law: the ratio of semichords for incident and refracted rays is constant. We then found that we had been beaten to this form of the law by nearly 400 years, by Descartes among others! Thus in the case of refraction, exemplary inquiry pedagogy has a counterpart in history. Note that the approach also reveals the underlying meaning of sine functions and a reason why trigonometry was invented. Students then go on to use the semichord representation to solve refraction problems by geometrical construction.

Footnotes:

None


