2.1

Hands On

With the objective of transferring an experiment from the physics and optics laboratories to a digital respectively virtual environment, the decision was made in favor of the promising experiment for measuring the specific charge of an electron e/m. This is based on the research of J. J. Thomson, who made the first quantitative statements about a cathode ray in 1897. For this purpose, he considered the deflection of the cathode rays in a magnetic field.⁴

Complementing Thomson’s experimental setup, Helmholtz coils are used to generate a homogeneous magnetic field. By adjusting the accelerating voltage V_acc and the current I in the coil of the magnetic field B, the specific charge can be measured by reading the diameter d of the electron beam. An approximation to the literature value of the specific charge can be determined with the repetition of the measurement process and the subsequent calculation. The figure 1 illustrates such a measurement step.¹

Figure 1.

Experiment to determine the specific charge of an electron. Photography by D. Curticapean.

2.2

Virtual Reality Application

A transformation of the presented experiment into a virtual environment is much more complex. This requires a three-dimensional reproduction of all objects involved. In this way, the experiment is carried out realistically in the virtual environment. This includes the Teltron tube and the associated voltage and current generators. A visual impression is given by the following image 2.³

Figure 2.

Virtual Teltron tube created with Blender.

3.1

Educational Goals

The proposed taxonomy of Bloom⁵ is used to define the educational goals. The taxonomy divides the learning objectives into six individual stages, which differ in complexity. In the figure 3 these stages are shown. The cognitive skill level can be consciously controlled as the stage increases.

Figure 3.

Bloom’s taxonomy. Source: B. S. Bloom⁵

The first stage of Bloom’s Taxonomy (Knowledge) is the transfer of knowledge to participants. Texts, images, videos, animations, etc. can be used for the transfer.

In the second stage, a review of the acquired knowledge takes place to test whether the participants have understood the learning objectives of the first stage.

The application phase involves the practical implementation of the acquired knowledge. Various options are available for this, such as practical experiments, scenarios or role plays and complex simulations. The focus should be on simulating real problems in order to apply the knowledge and skills learned.

The fourth stage describes the analytical decomposition of elements, relations and order structures based on their context and the subsequent extraction of the ideas, problems and differences.

In synthesis, the participant applies the ability to develop his or her own ideas and concepts based on the content learned.

The last stage of the taxonomy inspires the participant to use the acquired skills and knowledge to analyze and critically evaluate the learned content.

The developed application includes the first four stages of Bloom’s taxonomy.

3.2

Determination of e/m

In the virtual space, the physical properties of the experiment must be simulated. This ensures that the measured values in the virtual experiment correspond to reality and that their results are identical. Furthermore, an increased immersion can be achieved by a realistic simulation of the physical laws.⁶

At the beginning of the experiment, a voltage is applied to the electron beam generator, which emits electrons. The emitted electrons are accelerated with the voltage V_acc in the direction of the anode to a kinetic energy E_k of

and leave through a small gap and enter the glass sphere. In doing so, they have the following velocity v:

Inside the glass sphere, the electrons collide with argon atoms and ionize them. The kinetic energy is sufficient to put the argon atoms into a higher energy state. When the atoms fall back to their original state, photons are emitted and can be perceived by the human eye. The virtual realization of this visible effect is explained in more detail in the chapter 4.2.

A magnetic field is generated when the Helmholtz coils are switched on. This field acts perpendicular to the direction of velocity of the electrons. The existing Lorentz force F_L steers the electrons with the equation

The deflection of the electrons leads to the fact that the electrons are held on a circular path and the applied centripetal force F_C can be described with the radius r:

The ratio of the specific charge can be determined by equating the Lorentz force F_L with the centripetal force F_C. This ratio is composed of the charge of an electron and the mass of an electron, which is given by the following equation

The specific charge has a value of

which corresponds to the literature value.

3.3

Augmented Reality

In the context of this paper, the phrase augmented reality needs to be defined first. Today, there are several definitions. The best known one by Paul Milgram et al. will be discussed here.⁷ He theorizes that there are different kinds of realities, which are connected by a continuum. This extends from the real world to the virtual world. The figure 4 shows the corresponding schematic representation of the Reality-Virtuality Continuum.

Figure 4.

Reality–Virtuality Continuum schematic. Source: A. Benassi⁸

The functionality of augmented reality is limited to linking virtual information with the real world. This type of integration can be realized with the support of various display technologies that overlay and combine information with the user’s view.⁹

4.1

Nreal AR glasses

Augmented reality glasses serve as an interface between the real world and the virtually embedded information. The glasses fulfill two tasks. In the first task, the glasses record information from the real world via an integrated camera. In the second step, the collected data is processed for localization and orientation in the virtual space and forwarded to the corresponding subsystems. Finally, the virtual content is displayed on the glasses display.¹¹

The decision to use Nreal AR glasses can be justified by the following points:¹²

The developed prototype uses the supplied controller for input, which can be operated with one hand. This is shown in the figure 5 and supports control over 3 degrees of freedom. This includes 360 degree rotation around all three axes. The Nreal SDK library provided is used for software development.¹³

Figure 5.

Left: Controller front. Right: Controller back side. Source: Nreal Gitbook¹⁴

4.2

Immersive Visualization

In the Unity Engine, all objects, whether they are 3D models (meshes) or 2D models (sprites), are managed with so-called materials. These materials describe the visual properties and functions of a body. Technically, the materials are implemented with a shader. Each shader can be considered as a program developed specifically for the graphics card or other acceleration processor. Depending on the performance of the chosen device, the default shaders provided by the Unity engine can be used or custom optimized shaders must be developed. For the prototype, Unity’s default shaders will be used. However, it is recommended to replace the shaders with own implementations.¹⁵

The electron beam described in chapter Theoretical Background is visibly represented in the virtual environment by a two-dimensional line. In order for the electron beam to assume arbitrary curves, the line must be divided into several straight segments. High segmentation further approximates the individual line segments to the ideal curve. A demonstrative approximation is shown in the figure 6.¹⁶

Figure 6.

Virtual electron beam generated in Unity Engine.