The behavior of waves when they transition from one medium to another depends on the properties of the two media involved, particularly their respective wave speeds. Whether a wave travels from a faster medium to a slower medium or vice versa can be determined by comparing the wave speeds in each medium.
When a wave encounters a boundary between two media, it can undergo either refraction or reflection. Refraction occurs when the wave changes direction and speed as it passes from one medium to another at an angle. Reflection, on the other hand, happens when the wave bounces back upon encountering the boundary.
To determine the direction of wave propagation (from fast to slow or slow to fast), you need to consider Snell's law, which describes the relationship between the angles of incidence and refraction as well as the wave speeds in the two media. Snell's law states:
n1 * sin(θ1) = n2 * sin(θ2)
where: n1 and n2 are the refractive indices of the first and second media, respectively, θ1 is the angle of incidence (the angle between the incident wave and the normal to the boundary), and θ2 is the angle of refraction (the angle between the refracted wave and the normal to the boundary).
The refractive index of a medium is related to the wave speed in that medium. Generally, a higher refractive index corresponds to a slower wave speed.
If the wave is transitioning from a medium with a higher wave speed (lower refractive index) to a medium with a lower wave speed (higher refractive index), then Snell's law predicts that the angle of refraction (θ2) will be smaller than the angle of incidence (θ1). This indicates that the wave bends toward the normal (a line perpendicular to the boundary). In this case, the wave is traveling from a fast medium to a slow medium.
Conversely, if the wave is transitioning from a medium with a lower wave speed (higher refractive index) to a medium with a higher wave speed (lower refractive index), Snell's law predicts that the angle of refraction (θ2) will be larger than the angle of incidence (θ1). This indicates that the wave bends away from the normal. In this scenario, the wave is traveling from a slow medium to a fast medium.
By examining the relative angles of incidence and refraction, as determined by Snell's law, you can determine the direction of wave propagation when it encounters a boundary between two media with different wave speeds.