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

Refraction

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Rifrazione (refraction);
   • If you want to change the position of the source, select Stop and Cancella onde (clear waves).
   • With the mouse, drag the ends of the plane wave (the two blue circled crosses) to the desired positions.
   • Deselect Stop

     We suggest you:

     • change the angle between the plane wave and the boundary surface
     • try putting the source of the wave inside the blue medium
     • try orienting the plane wave parallel to the boundary surface
2. Remarks
   • By "default" the program starts in a configuration whose source is a plane wave propagating at a certain angle to the boundary surface. The reflected ray is visible, and the refracted ray bends towards the normal to the boundary surface. Changing the position of the source as suggested, you will see that:
   • when the source is inside the medium with the higher refractive index, the ray bends away from the normal;
   • when the wavefront is parallel to the boundary surface, there is no deviation of the direction of propagation, but precisely for this reason the only thing you see is the change of wavelength (not of frequency) in passing from one medium to the other.
3. Related topics: see refraction, refractive index, refraction in one dimension (in Italian)
4. To find out more: see impedance, impedance matching, waves and rainbows, refraction of sound

Total reflection

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Rifrazione totale (total refraction);
   • If you want to change the position of the source, select Stop and Cancella onde (clear waves).
   • With the mouse, drag the ends of the plane wave (the two blue circled crosses) to the desired positions.
   • Deselect Stop
     • We suggest you change the angle between the plane wave and the boundary surface until refraction appears again.
2. Remarks
   • By "default" the program starts in a configuration in which the wavefront strikes the surface at an angle greater than the critical angle. In this configuration there should be only reflection. In fact a weak refracted wavefront also appears, due to the spherical waves generated by the end points of the plane wave (which strike the surface at a less grazing angle).
3. Related topics: see refraction, refractive index, refraction in one dimension (in Italian)
4. To find out more: see impedance, impedance matching, waves and rainbows, refraction of sound

Total reflection from a circular prism

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Rifrazione prisma circolare (refraction: circular prism);
   • Select Stop and Cancella onde (clear waves);
   • In the second drop-down menu (from the top) select 1 sorgente 1 frequenza (1 source, 1 frequency);
   • With the mouse, drag the source into the circular region with the higher refractive index, close to the centre of the region.
   • Deselect Stop. What do you see?
   • Select Stop and Cancella onde (clear waves);
   • With the mouse, now drag the source within the circular region to a point close to the interface.
   • Deselect Stop. What do you see?
2. Remarks
   • By "default" the program starts in a configuration in which the source is a plane wave, and the wavefronts refracted by the circular region are shown. The suggested changes let you check the phenomenon of total reflection in a spectacular way: when the source is inside the medium with the higher refractive index and close to its walls, the wave it generates can get out only at certain angles of incidence (not too grazing). Note that when the source is close to the centre of the circular region, the angles of incidence are not large enough to cause total reflection, and the refracted wave comes out in every direction.
3. Related topics: see refraction, refractive index, refraction in one dimension (in Italian)
4. To find out more: see impedance, impedance matching, waves and rainbows, refraction of sound

Mirages and other strange phenomena

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Rifrazione: miraggio (Refraction: mirage);
     • if you have problems due to the low brightness of the colours, increase the brillantezza (brightness) with the slider of the same name
   • Have fun moving the source by dragging it with the mouse. This will produce a confused image, due to the superposition of the waves generated by the source in its various positions
   • To see the phenomenon more clearly, restart the animation from the beginning by selecting "Cancella onde" (clear waves)
   • Insert a vertical wall, about one centimetre from the source, starting from the top edge of the window and ending just below the height of the source. To do this:
     • select Stop;
     • in the Funzioni del Mouse (mouse functions) menu select Mouse=modifica pareti (mouse = edit walls)
     • build the wall by dragging the mouse, with the right button pressed, over the region of interest
2. Remarks
   • By "default" the program starts in a configuration in which the physical space reached by the wave has a region (coloured black) with a decreasing refractive index. The change of direction of the wave is clearly visible: an observer on the left will believe that the ray comes from the black region and not from the real position of the source: this is what we have called an inferior mirage. Inserting the wall reveals a peculiar feature of waves: their ability to get past obstacles (in this case this ability is due not to diffraction but precisely to the change in refractive index).
3. Related topics: see refraction, refractive index, refraction in one dimension (in Italian)
4. To find out more: see impedance, impedance matching, waves and rainbows, refraction of sound
5. Other experiments

You can try other types of mirage, obtained by varying the refractive index in different ways, by selecting at the top left

• Rifrazione:inversione termica (Refraction: thermal inversion)

This demonstration reproduces quite faithfully a well-known sound mirage due to particular conditions of thermal inversion in the atmosphere. For a full illustration of the phenomenon see refraction of sound.

• Rifrazione:gradiente termico 1 (Refraction: thermal gradient 1)
• Rifrazione:gradiente termico 2 (Refraction: thermal gradient 2)

Watch carefully and try to work out how the refractive index varies in the various regions.