Critical angle

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The critical (angle of incidence) is a term from physics and is used in connection with the refraction of waves . The term is particularly common in optics and refraction seismics .

description

Total reflection (red and yellow): Internal reflection when light strikes from the optically denser medium to an optically thinner medium ( Goos-Hänchen effect is neglected)

optics

The refraction of waves, i.e. the change in direction of the course when a wave passes from one medium to an adjacent medium, is based on a change in its speed of propagation . This is determined by the medium traversed. For example, consider an electromagnetic wave (such as visible light) that propagates in a medium 1 and hits an interface with a medium 2 at a known angle of incidence . According to the Fresnel equations , this is partly reflected or transmitted, that is, the light passes into the medium 2. During this transition the light beam (can be viewed as interference of the light waves) undergoes a change of direction according to Snell's law of refraction , it is "refracted" (green beam path in the picture).

For a transition from a medium 1 to an optically denser medium 2 ( , ), this means that the beam is refracted towards the perpendicular , for example when moving from air to water. , stand for the speed of propagation and , for the refractive index of the two media.

In the opposite case (the light beam comes from the water), however, it is refracted away from the perpendicular. If you increase the angle of incidence , the refracted ray runs parallel to the boundary surface from a certain value (yellow ray path). This angle is called the critical angle of total reflection or critical angle . In other words, the critical angle is the angle at which transmission no longer occurs (or barely because the propagation speed of the critically refracted wave is that of the medium into which it would be transmitted (the faster one)). The angle of total reflection can be calculated with the help of Snell's law of refraction:

Seismics

The dependence of the beam path on the speed of propagation also applies to seismic waves . In this case of mechanical wave propagation, the “wave beam” represents the vertical trajectory of the wave front . If the speed of propagation changes, this changes the position of the wave front and thus also the beam path. In seismics, Snell's law of refraction is defined by the propagation speeds ( , ) of the media passed through:

which is completely equivalent to the formulation of optics with the refractive index, if one considers that (with the speed of light and the speed of propagation in the respective medium):

The critical angle must therefore be calculated from:

In contrast to electromagnetic waves, the speed of which - as explained using the example of a light beam - decreases in the optically denser medium, in seismic waves this increases when the wave front enters a more compact medium. A critical refraction therefore occurs in seismic waves at the transition from a looser to a firmer rock.

The seismic critical refraction effect is specifically exploited in the refraction seismic method to investigate the layer structures of the earth's interior: As a rule, the seismic speeds increase with increasing depth, so that when a seismic wave hits a layer boundary below the critical angle, a refracted wave is created . This so-called head wave propagates along the layer boundary at the speed of the lower layer. It continuously emits seismic wave energy, which in turn runs back to the surface at the critical angle, where it is recorded and can be used to determine the speed of propagation.

literature