  The propagation and refraction of waves in dispersive media are considered. A
primary objective is to determine whether waves refract as monochromatic waves
by Snell's law with phase velocity or as wave packets. The refraction of wave
packets requires two refraction laws. The wave packets refract according to
Snell's law with the geometric group velocity while the wavelets within the
wave packets refract according to Snell's law with phase velocity. The tests
were performed using directional power spectra from gravity water waves
originating in the Caribbean Sea, Gulf of Mexico, Indian Ocean, and the
Southern Ocean. In all cases the waves were measured with arrays of pressure
sensors. It was found that the refraction of monochromatic waves led to
backtracks from a measurement site that spread out for the different wave
periods and did not go back to a common source. When the refraction was large
the results were especially bad. When the data were used to test the refraction
of wave packets very good results were obtained. For every storm considered the
backtracks of the different wave periods went back together to the wave
generation area. These results offer strong support for refracting waves in
dispersive media as wave packets, not as monochromatic waves. This result for
wave groups was also determined in a controlled wave tank experiment of gravity
water waves where a critical angle was tested. The properties of propagating
wave packets are also considered and illustrated. Reflection points and
critical angles are found and explained. There can be major differences between
the propagation of wave packets and monochromatic waves.
