The limitations of Snell's law in the design of ultrasound transducers

Because the refracted sound field of a finite beam extremely depends on the size and on the frequency of the generating element, Snell's law is not applicable to calculate the refraction angle of a finite beam. Approaches using plane reflection and transmission coefficient in connection with a discretization of the source into elementary point sources are more exact. This paper demonstrates that the application of plane reflection and transmission coefficients requires a point to point distance smaller than a half wavelength, in order to obtain an accurate sound field of the refracted beam.