The angle of a refracted transverse wave depends on which property across the interface?

• A. The Velocities of the Materials On Each Side of the Interface
• B. The Surface Roughness
• C. The Temperature
• D. The Material Densities

Answer: (A)

When a wave crosses an interface, the direction of the refracted wave is set by how fast the wave travels in each medium. The relation that governs this is Snell’s law, which links the incident angle, the refracted angle, and the speeds in the two media: sin(theta_in) / v1 = sin(theta_out) / v2. This means the angle of refraction depends on the velocities of the materials on either side of the boundary (the speed contrast). Surface roughness, temperature, and density don’t directly determine the refracted angle in the same way; roughness affects scattering and amplitude, temperature can slightly shift speeds but isn’t the primary factor, and density alone doesn’t set the refraction angle without considering the resulting speeds.