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Refraction and Snell's law at interfaces

An ultrasound beam crosses a horizontal boundary between two media. In the upper medium (speed c1) an incident beam meets the boundary obliquely at angle theta 1 to the normal. In the lower, faster medium (speed c2 greater than c1) the transmitted beam bends away from the normal at a larger angle theta 2, following sin theta1 over c1 equals sin theta2 over c2. A dotted line shows the straight path the scanner assumes, illustrating that refraction displaces echoes and causes a spatial artefact.

Refraction of an ultrasound beam at a boundary (Snell's law) An ultrasound beam crosses a horizontal boundary between two media. In the upper medium (speed c1) an incident beam meets the boundary obliquely at angle theta 1 to the normal. In the lower, faster medium (speed c2 greater than c1) the transmitted beam bends away from the normal at a larger angle theta 2, following sin theta1 over c1 equals sin theta2 over c2. A dotted line shows the straight path the scanner assumes, illustrating that refraction displaces echoes and causes a spatial artefact. boundary normal incident beam refracted beam assumed straight path θ₁ θ₂ medium 1 — speed c₁ medium 2 — speed c₂ (c₂ > c₁) sin θ₁ / c₁ = sin θ₂ / c₂ c₂ > c₁: beam bends away from normal (θ₂ > θ₁) Oblique incidence with differing speeds displaces echoes along the assumed path — a spatial artefact (misregistration). Critical angle: θ₂ = 90° (refracted beam runs along the boundary), possible only when c₂ > c₁. No bending at normal incidence.
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