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Ultrasonic Inspection - Snell's Law

Snell's Law is used regularly when performing angle beam inspections.  Snell's Law describes the relationship between the incident and refracted angles of a wave as it moves from one material into another material which has a different wave velocity.  Refraction takes place at the interface due to the different velocities of the acoustic waves within the two materials. Snell's Law equates the ratio of material velocities V1 and V2 to the ratio of the sine's of incident (Q1) and refracted (Q2) angles.

 

Snell's Law is usually presented in the form of one of the following equations. 

    OR      

The first equation states that the ratio of the sine of the incident angle and the wave velocity in material 1 is equal to the ratio of the sine of the refracted angle and the wave velocity in material 2.  The second equation states that the ratios of the sine's of the two angles is equal to the ratio of the two velocities.  It should be evident that the two equations are equivalent.

Example Calculations

1) What is the incident angle that will produce a 70 degree refracted shear wave in steel using a Lucite wedge.

First establish the values.

  • Q1= the value to be determined
  • Q2= 70 degrees
  • V1= 0.106 in/ms (sound velocity of a longitudinal wave in Lucite)
  • V2= 0.128 in/ms (sound velocity of a shear wave in steel)

Plug the known values into the equation.

    becomes      

Simplify by dividing the right side of the equation

Determine the sine of 70 degrees with a calculator or lookup table.

Multiply both sides of the equation by 0.940 to solve for Sin q

Finally, take the inverse sine of 0.778 to determine the angle whose sine equal 0.778.

Q2 = 51.1 degrees

 

2) If the incident angle is 24 degrees when setting up an immersion inspection, what is the refracted shear wave angle in aluminum?

First establish the values.

  • Q1= 24 degrees
  • Q2= the value to be determined
  • V1= 0.148 cm/ms (sound velocity of a longitudinal wave in water)
  • V2= 0.313 cm/ms (sound velocity of a shear wave in aluminum)

Determine the sine of 24 degrees with a calculator or lookup table.

Sin 24 = 0.407

Plug in this value and cross multiply and divide.

Finally, take the inverse sine of 0.861 to determine the angle whose sine equal 0.861.