Abstract:

Many science and engineering students feel threatened by mathematics. Many times this is an irrational fear but in some cases the mathematical artillery needed to solve a physical problem is truly formidable for the students.

The use of computer software opens a whole new world of possibilities in simulating physical phenomena and allows us to analyze in the classroom non-trivial problems from a mathematical point of view. We present in this paper a Mathematica® [1] notebook we have written to simulate several one- and two- dimensional Fraunhofer diffraction patterns.

The student can change the size and shape of the diffracting system as well as the radiation frequency. So, it is possible to study very easily the way the diffraction pattern changes as those parameters vary. We have also defined an approximate color scale to see the patterns as they would appear in a real life experiment. This approach has the advantage of presenting the student with a range of light frequencies impossible to get in a laboratory.

The notebook we have developed calculates and represents the diffraction pattern from a round, rectangular or triangular hole as well as from a double slit and from an arbitrary set of slits. This last example allows the student to understand the way a grate diffracts light.

Besides, our code is very easy to adapt to other physical or mathematical problems dealing with Fourier transforms. This area of mathematics is very difficult to visualize for the students but our notebook makes this visualization much easier. It allows the students to focus on the physical properties of the phenomena driven by these kind of transforms (not only in optics but also for instance in quantum mechanics) without getting lost in the cumbersome mathematical details.

References:
[1] www.wolfram.com

Keywords:

Computer simulation, difraction, Mathematica.