# Animation of Wave Dispersion

This animation shows a traveling pulse of light. In air, the wavelength of the light is 800 nm, and the envelope of the pulse is Gaussian with a half-width at half-maximum equal to 1.5 um (micrometers). The time duration of the pulse as it passes is 5 fs. The width of the screen is 20 um. A number in the upper lefthand corner of the screen shows the position of the pulse (the center of its Gaussian envelope). When the animation begins, the pulse is frozen in time 50 um from the surface of a piece of glass. The index of refraction of the glass is given by n=n0+n1(w/w0), where w is the angular frequency of the wave, w0 is the angular frequency of a 800-nm wave, and n0=1.4948 is the index of refraction of the glass at 800 nm. The value of n1 in glass is 0.016.

The program recognizes the following commands:
 S Slow. The wave starts to move at the speed of light. We follow along with the wave, viewing it in slow motion. The blue background represents air, and the red background represents glass. As the wave enters the glass, it slows down and becomes narrower (at first). F Fast. View the wave in fast motion. Now we can see the difference between the phase velocity (the velocity of the waves inside the envelope) and the group velocity (the velocity of the envelope). We also see that the pulse broadens with time, the long-wavelength component of the pulse moving faster than the short-wavelength component of the pulse. Note that the wavelength of the wave at the front of the pulse becomes noticeably longer than the wavelength of the wave at the rear of the pulse. R Restart. Put the pulse back in air 50 um from the glass. It sits there until either an S or F is pressed. P Pause. Stop the animation. Press any key to resume animation. Q Quit program. ? Help. These commands are listed.