Snells Law

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

This online tool below will calculate either one of the following:

  • Incident angle
  • Incident material velocity
  • Refracted angle
  • Refracted material velocity

given that 3 of the 4 are supplied

Incident Angle (°):
Incident Velocity (m/s):
Refracted Angle (°):
Refracted Velocity (m/s):


Beam angles should always be plotted using the appropriate industry standard, however, knowing the effect of velocity and angle on refraction will always benefit an NDT technician when working with angle inspection or the immersion technique.

The above calculator uses the following equation:

ultrasonic snells law formula


A1 = The angle of incidence.

V1 = The incident material velocity

A2 = The angle of refraction

V2 = The refracted material velocity

Example 1:

Suppose you wish to calculate the refracted angle within a material when you know the incident angle (20°), incident material velocity (2330 m/s) and refracted material velocity (5960 m/s):

A1 = 20°

V1 = 2330 m/s

A2 = We dont know!

V2 = 5960 m/s

Subsituting these figures into the equation above gives us:

ultrasonic snells law formula

We cross multiply the fractions to give us

ultrasonic snells law formula


ultrasonic snells law formula


beamspread example eq4


beamspread example eq5


beamspread example eq6


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