When
an ultrasounic wave passes through an interface between two materials
at an oblique angle, and the materials have different indices
of refraction, both reflected and refracted waves are produced.
This also occurs with light, which is why objects seen across
an interface appear to be shifted relative to where they really
are. For example, if you look straight down at an object at the
bottom of a glass of water, it looks closer than it really is.
A good way to visualize how light and sound refract is to shine
a flashlight into a bowl of slightly cloudy water noting the refraction
angle with respect to the incident angle.
Refraction takes place at an interface due to the different
velocities of the acoustic waves within the two materials. The
velocity of sound in each material is determined by the material
properties (elastic modulus and density) for that material. In
the animation below, a series of plane waves are shown traveling
in one material and entering a second material that has a higher
acoustic velocity. Therefore, when the wave encounters the interface
between these two materials, the portion of the wave in the second
material is moving faster than the portion of the wave in the
first material. It can be seen that this causes the wave to bend.
Snell's Law describes the relationship between the angles and
the velocities of the waves. Snell's law equates the ratio of
material velocities V1 and V2 to the ratio of the
sine's of incident (Q1)
and refracted (Q2)
angles, as shown in the following equation.
Where:
VL1 is the longitudinal wave velocity in material
1.
VL2 is the longitudinal wave velocity in material
2.
Note that in the diagram, there is a reflected longitudinal wave
(VL1' ) shown. This wave is reflected at the
same angle as the incident wave because the two waves are traveling
in the same material, and hence have the same velocities.
This reflected wave is unimportant in our explanation of Snell's
Law, but it should be remembered that some of the wave energy
is reflected at the interface. In the applet below, only the incident
and refracted longitudinal waves are shown. The angle of either
wave can be adjusted by clicking and dragging the mouse in the
region of the arrows. Values for the angles or acoustic velocities
can also be entered in the dialog boxes so the that applet can
be used as a Snell's Law calculator.
When a longitudinal wave moves from a slower to
a faster material, there is an incident angle that makes the angle
of refraction for the wave 90o. This is know as the first critical
angle. The first critical angle can be found from Snell's law
by putting in an angle of 90° for the angle of the refracted
ray. At the critical angle of incidence, much of the acoustic
energy is in the form of an inhomogeneous compression wave, which
travels along the interface and decays exponentially with depth
from the interface. This wave is sometimes referred to as a "creep
wave." Because of their inhomogeneous nature and the fact
that they decay rapidly, creep waves are not used as extensively
as Rayleigh surface waves in NDT. However, creep waves are sometimes
more useful than Rayleigh waves because they suffer less from surface irregularities and
coarse material microstructure due to their longer wavelengths.
When
an ultrasounic wave passes through an interface between two materials
at an oblique angle, and the materials have different indices
of refraction, both reflected and refracted waves are produced.
This also occurs with light, which is why objects seen across
an interface appear to be shifted relative to where they really
are. For example, if you look straight down at an object at the
bottom of a glass of water, it looks closer than it really is.
A good way to visualize how light and sound refract is to shine
a flashlight into a bowl of slightly cloudy water noting the refraction
angle with respect to the incident angle. 
