Snells Law, Refraction and Reflection

Like light, when an incident ultrasonic wave encounters an interface to an adjacent material of a different velocity, at an angle other than normal to the surface, then both reflected and refracted waves are produced.

Understanding refraction and how ultrasonic energy is refracted is especially important when using angle probes or the immersion technique. It is also the foundation formula behind the calculations used to determine a materials first and second critical angles.

First Critical Angle

Before the angle of incidence reaches the first critical angle, both longitudinal and shear waves exist in the part being inspected. The first critical angle is said to have been reached when the longitudinal wave no longer exists within the part, that is, when the longitudinal wave is refracted to greater or equal than 90°, leaving only a shear wave remaining in the part.

Second Critical Angle

The second critical angle occurs when the angle of incidence is at such an angle that the remaing shear wave within the part is refracted out of the part. At this angle, when the refracted shear wave is at 90° a surface wave is created on the part surface

Formula

The relationship between the angle of the incident and refracted sound waves is descibed by the following formula:

Sin(A1)/V1 = Sin(A2)/V2

Where

A1 = The incident sound wave angle in degrees
V1 = The acoustic velocity of the incident material in metres per second
A2 = The refracted sound wave angle in degrees
V2 = The acoustic velocity of the refracted material in metres per second

By simple arrangment the formula may be changed to find any one of the values, provided that the other three unknown values are supplied.

E.g. To find the refracted angle, given the incident angle and velocity and the refracted material velocity the equation is rearranged as below:

V2 * (Sin(A1)/V1) = Sin(A2)

Getting the inverse of the answer, that is the inverse of Sin(A2) will return the angle in degrees of the refracted angle.

by Michael K Penn