Use Curvenote - logo

NPM Version MIT License GitHub Stars Twitter Follow

Snell's Law

Angles Of Reflection And Refraction

Consider a P-wave which is incident at an angle $\theta_1$ measured with respect to the normal of the interface, as seen in the figure below where the approaching wave is represented as a ray. The angles of the reflected and refracted rays are as follows:

If the wave travels from a low velocity medium to a high velocity medium the wave gets refracted away from the normal. Conversely, it gets refracted toward the normal if the wave goes from a high velocity to a low velocity medium.

$\theta_1$: °
$\theta_2$: No Refraction Wave°
$v_1$: m/s
$v_2$: m/s

Snell's Law for two layers where $v_1$= m/s and $v_2$= m/s. The incident angle of the incoming wave is $\theta_1$= °. When an incident wave has an angle over the critical angle, $\theta_c$, there is no refracted wave.

The critical refraction angle, called $\theta_c$, is a key concept in refraction seismology. This is the angle of incidence for which the corresponding angle of refraction is 90°. In this case, the refracted ray travels horizontally along the interface. A formula for the critical angle can be derived from Snell's law as follows:

\frac{\sin \theta_c}{v_1} = \frac{\sin 90^{\circ}}{v_2} = \frac{1}{v_2}

Made with love by Curvenote
Last updated February 19th, 2021