 Home - Education Resources - NDT Course Material - Ultrasound  - Introduction to Ultrasonic Testing Introduction Basic Principles History Present State Future Direction Physics of Ultrasound Wave Propagation Modes of Sound Waves Properties of Plane Waves Wavelength/Flaw Detection Elastic Properties of Solids Attenuation Acoustic Impedance Reflection/Transmission Refraction & Snell's Law Mode Conversion Signal-to-noise Ratio Wave Interference Measurement Techniques Normal Beam Inspection Angle Beams I Angle Beams II Crack Tip Diffraction Automated Scanning Velocity Measurements Measuring Attenuation Spread Spectrum Signal Processing Flaw Reconstruction Selected Applications Rail Inspection Weldments Reference Material UT Material Properties References Quizzes

Refraction and Snell's Law When an ultrasonic 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.  