Ultrasonic
Snell's law: refracted angle
The refracted angle in the part from the wedge angle and the two velocities, the wedge angle for a refracted angle you want, and the critical angles.
For reference only — verify against your procedure and the governing code.
Acrylic is 2.670 mm/µs typical (ASTM E494).
Steel shear is 3.230 mm/µs typical.
ASTM E494 Table X3.1 typical values, converted from the source's m/s.
Result
- Refracted angle
- 45.32°
- Wedge angle for the wanted angle
- 35.77°
- 1st critical angle (longitudinal)
- 26.91°
- 2nd critical angle (refracted mode above)
- 55.75°
Formula
- sin θ₁ / V₁ = sin θ₂ / V₂
- Critical angle: θc = asin(V₁ / V₂)
Units. Velocities in mm/µs (= km/s) or in./µs. Snell's law uses only their ratio, so the angles are the same in either system.
Assumptions and limits
- Angles measured from the normal to the surface. Velocities are typical unless measured (ASTM E494 Table X3.1 selection); real wedges and materials vary.
- A refracted angle beyond 90° means no refracted wave of that mode — past the critical angle.
Sources
- ASTM E587-20, Standard Practice for Ultrasonic Angle-Beam Examination by the Contact Method — §4.1–4.2 refraction; §4.3.3 wavelength = velocity / frequency.
- ASTM E494-20, Standard Practice for Measuring Ultrasonic Velocity in Materials — Appendix X3, Table X3.1 (typical values).
More ultrasonic calculators
For reference only — verify against your procedure and the governing code.
Standards and documents are cited by their publishers' names to identify them. TRACE is not affiliated with, endorsed by or sponsored by ASTM International, ASME, the U.S. Nuclear Regulatory Commission, NIST or the Laboratoire National Henri Becquerel. Formulas are paraphrased and cited by clause; get the documents themselves from their publishers.