Critical angles: what it means and why it matters

Where they come from

Snell's law relates the angles and velocities on both sides of a boundary: sin θ1 / c1 = sin θ2 / c2. In a wedge on steel, θ1 is the incident angle in the wedge and c1 is the wedge velocity. The refracted longitudinal wave in steel travels faster than the refracted shear wave, so it bends further from the normal as the incident angle grows. It reaches 90 degrees first, at the first critical angle. The shear wave reaches 90 degrees later, at the second.

A worked example

Use made-up but realistic values: a wedge material with a longitudinal velocity of 2.70 mm/µs, steel with a longitudinal velocity of 5.90 mm/µs and a shear velocity of 3.20 mm/µs.

• First critical angle: sin θ = 2.70 / 5.90 = 0.458, so θ is about 27.2 degrees.
• Second critical angle: sin θ = 2.70 / 3.20 = 0.844, so θ is about 57.5 degrees.

A wedge with an incident angle between those two values sends only a shear wave into the steel. That is why standard shear wave angle beam wedges are cut with angles inside that range, and why the refracted shear angle in steel is the number printed on the probe, not the wedge angle.

The three zones

• Below the first critical angle: both longitudinal and shear waves enter the steel, and the screen can show confusing echoes from both.
• Between the two: only the shear wave enters. This is the working range for angle beam testing.
• Past the second: no shear wave enters. Energy can travel along the surface as a surface wave, which is used for surface-breaking flaws.

Mix-ups to avoid

• Wedge angle versus refracted angle. The critical angles are incident angles in the wedge. The probe label gives the refracted angle in the test material.
• Same numbers for every setup. The values depend on both materials. A different wedge or a different test material gives different critical angles.
• Which wave first. Longitudinal reaches 90 degrees first because it is faster. If the order feels backwards, think about which velocity is larger.

How the exam uses it

Critical angles appear under techniques and weldment evaluation, as Snell's law calculations and as questions on which wave modes exist at a given incident angle. Work the ratio of sines, then use the inverse sine, and keep all angles measured from the normal.

Topic names here follow the UT General outline for exams before 5 February 2027; the UT outline change guide shows how the later list lines up.

Practice it

Check the angle sums in the Snell's law calculator, then work the worked example in the UT formulas guide. The wave that survives is described in shear vs longitudinal waves, and what its angle does to the geometry is in skip distance. All terms are in the NDT terms glossary.

Know the term? Check the rest of the UT General topics

Take the free 10-question check. It covers the UT General exam, needs no signup and explains every answer, so you see which topic to study next. The course then adds timed practice exams and a study plan built from your exam date.

Sources

Show the list

Background reading: Evident's published UT material and ASNT's published topic headings. Outline checked 25 October 2026.

• Evident, ultrasonic flaw detection tutorial
• Evident, ultrasonic transducer technical notes
• ASNT NDT Level II examinations, published topic headings.

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