Abstract:

The conic curves have mathematical properties of great interest. As an example, let's take the straight segments from any point P of an ellipse to its two foci. It is well known that the sum of the lengths of these segments is constant for any P. However, it is not so known that the bisector of both segments is perpendicular to the ellipse. The two mentioned properties have an important consequence in Physics: the rays of any wave emitted from a focus, after being reflected in an elliptical surface, converge simultaneously in the other focus, and they do in phase. Parabolas and hyperbolas also have relevant properties in wave reflection. The behavior of the rays after being reflected in a conic curve has important applications such as the parabolic antennas in telecommunications or radio-telescopes and the extracorporeal shockwave lithotripsy in medicine.

In this work, we present a user-friendly virtual laboratory (developed using the tool “Easy Java Simulations”) to facilitate the visualization and understanding of the behavior of waves that are reflected in a conic curve. The user can choose the type of curve (ellipse, parabola or hyperbola) and its characteristic parameters (for example, the position of the foci), both by numerical input and by moving handles with the mouse. After introducing the parameters, an animation shows the rays and wave-fronts that start from a focus, how they evolve until they reflect in the curve, and what happens from that moment. In this way, the process is visualized, and the user can analyze how it is affected by the selection of the different parameters.

In order to increase the audience, the virtual laboratory offers the possibility of changing the interface language to English, Spanish or Valencian.

Keywords:

Virtual laboratory, Easy Java, waves, wave reflection, conic curves, parabolic antennas.