Abstract:

One of the most widely used methods for determining the focal length of a converging lens is the conjugate foci method. It was proposed by Friedrich Wilhelm Bessel and, therefore, it is known as Bessel’s method. Its success in optics laboratories at the undergraduate level is based on two facts: The underlying mathematical explanation is quite simple, and its practical implementation is easy and inexpensive. Nevertheless, students don’t always have access to an optics lab (for instance, if they are following an on-line course) and even if they do have access to one, their time there is limited. It is then interesting to provide them with a tool capable of recreating as close as possible to reality the experimental conditions and the observational results. Our challenge was creating an applet resembling the experimental setup so much that the same laboratory manual used in the lab could be used with the application.

We have developed a realistic simulation of the conjugate foci method written as a Mathematica notebook. We have selected this program because it uses the very powerful Wolfram Language and besides there is a free tool called Wolfram Player available for Windows, Linux, MacOS and iOS that allows students to use the notebook interactively. The student can select the height of the object, the distance from the object to the screen and the position of the lens using sliders and the applet shows in real time the configuration of the optical bench, as well as the image formed on the screen (including defocus or blur).

Keywords:

Optics virtual lab, Bessel’s method, Mathematica, Wolfram Language.