Snell’s Law Calculator

Understanding Snell's Law in Ultrasonic Testing

When an ultrasonic wave passes from one material into another at an angle, its speed changes. This change in velocity causes the sound beam to bend, or refract, according to Snell's Law.

In angle beam ultrasonic testing, a longitudinal wave generated inside the probe wedge enters the test material and changes direction as it crosses the interface. Depending on the materials and the incident angle, part of the energy continues as a longitudinal wave while another portion converts into a shear wave. This process is known as mode conversion and forms the basis of most angle beam inspections.

What Is Mode Conversion?

Mode conversion occurs whenever an ultrasonic wave crosses the boundary between two different materials at an angle. As the wave enters the test material, its energy is divided into different wave types:

• A refracted longitudinal wave
• A refracted shear wave
• Small reflected wave components

For most weld inspections, the refracted shear wave is the wave of interest because it provides excellent sensitivity to common weld discontinuities.

Critical Angles & Snell's Law

Critical Angles

Two important angles determine how ultrasonic waves behave as they enter the test material.

First Critical Angle: The first critical angle is reached when the refracted longitudinal wave travels along the material surface at 90°. Beyond this point, the longitudinal wave no longer propagates into the material, leaving the shear wave as the dominant inspection beam.

Second Critical Angle: The second critical angle occurs when the refracted shear wave also reaches 90°. Beyond this angle, neither refracted longitudinal nor refracted shear waves enter the material, making conventional angle beam inspection impractical.

Snell's Law Formula

The relationship between the incident and refracted angles is defined by Snell's Law:

• θ₁ = Incident angle in Material One
• θ₂ = Refracted angle in Material Two
• V₁ = Sound velocity in Material One
• V₂ = Sound velocity in Material Two