Modeling in Geometric Optics
In this project the students will simulate the uniform reflection property of a parabolic surface. That is, they will use the law of reflection along with finding slopes of tangent lines using calculus method and illustrate that a ray of light emanating from the focus of a parabola and hitting the parabola will be reflected in the direction of the axis of the parabola.
Students will learn modeling physical laws by using programming, which is the ultimate goal of numerical computations. MATLAB will be used to illustrate the uniform reflection property of parabolas which can be proved analytically.
Context for Use
This project is assigned for undergraduate students who have completed Calculus III as a research activity in mathematical modeling of geometric optics. The students are exposed to basic laws of geometric optics and are asked to used calculus method to prove the reflection property of parabola. The students will be asked to go through a Coursera course in Matlab before the beginning of the activity. They should be able to write a code with loops, if-else statements, plots etc.
Description and Teaching Materials
reflection property of parabola (Acrobat (PDF) 118kB Aug19 19)
Project (Acrobat (PDF) 50kB Aug19 19)
Teaching Notes and Tips
correctness of the program, flexibility to change of values of parameters, output demonstration.