The app controls are labelled in Italian: below, each label is given as it appears in the app, followed by its English meaning.

Reflection from a plane mirror

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Rifrazione (refraction): the app shows both the refracted ray and the reflected ray.
   • If you want to remove the refracted ray, create a wall with the mouse (right-click to choose the "modifica pareti" (edit walls) mode)
   • Left-click and drag along the wall you want to create (we suggest the interface between the black and the blue region)
   • you can change the position of the sources by selecting Stop and Cancella Onde (clear waves); two "crosshairs" will appear, which are the ends of the plane wave; change their position by dragging them with the mouse.
   • to restart the animation deselect Stop
2. Remarks
   • The equality of the angles of incidence and reflection is evident, and does not depend on the frequency of the incident wave (you can check this by changing the frequency of the source with the command of the same name).

Reflection from a parabolic mirror

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Riflessione: specchio parabolico 1 (Reflection: parabolic mirror 1)
   • If the wave is not clearly visible, increase its Brillantezza (brightness) using the slider of the same name;
   • Increase the frequency of the wave using the Frequenza sorgente 1 (source 1 frequency) slider;
2. Remarks
   • The initial configuration shows very clearly that the wave generated by a point source placed at the focus of the parabola forms, once reflected, a plane wave (with wave rays parallel to the axis of the parabola). If you want to see in more detail how the circular wavefront of the source turns into a plane wavefront
   • select in the second menu (from the top) 1 Sorgente, 1 Freq (impulso) (1 source, 1 frequency (pulse))
   • reduce the frequency of the pulse to the minimum and increase the Brillantezza (brightness) using the sliders of the same name.
   • you can also check that the focus is the only point with the observed properties: select Stop and Cancella Onde (clear waves) and move the source with the mouse to a point other than the focus. To restart the animation deselect Stop: you will see that the reflected wavefronts are no longer exactly plane.
   • As the frequency of the wave increases, dark fringes appear, due to destructive interference between the waves generated by the source and the waves reflected by the mirror. To understand why this happens only at high frequencies (short wavelengths), you can visit the page mathematical aspects of interference.
3. Other experiments
   • By selecting at the top left Riflessione: specchio parabolico 2 (Reflection: parabolic mirror 2) you can see that the phenomenon is reversible: plane waves with wave rays parallel to the axis of symmetry of the parabola are concentrated at the focus of the parabola (this is the property exploited by satellite dishes).
   • By selecting at the top left Riflessione: cavità ellittica (Reflection: elliptical cavity) you can see that the focus of the ellipse also has remarkable properties: the waves coming from one focus of the ellipse are concentrated at the second focus.