As θ increases beyond θc, the refracted ray disappears and only the reflected ray remains, so that all of the energy of the incident ray is reflected; this is total internal reflection (TIR). In brief: If θ < θc, the incident ray is split, being partly reflected and partly refracted; If θ > θc, the incident ray suffers total internal reflection (TIR); none of it is transmitted. Critical angle The critical angle is the smallest angle of incidence that yields total reflection, or equivalently the largest angle for which a refracted ray exists. For light waves incident from an "internal" medium with a single refractive index , to an "external" medium with a single refractive index , the critical angle is given by and is defined if . For some other types of waves, it is more convenient to think in terms of propagation velocities rather than refractive indices. The explanation of the critical angle in terms of velocities is more general and will therefore be discussed first。 When a wavefront is refracted from one medium to another, the incident (incoming) and refracted (outgoing) portions of the wavefront meet at a common line on the refracting surface (interface). Let this line, denoted by L, move at velocity across the surface, where is measured normal to L (Fig.4). Let the incident and refracted wavefronts propagate with normal velocities and (respectively), and let them make the dihedral angles θ1 and θ2 (respectively) with the interface. From the geometry, is the component of in the direction normal to the incident wave, so that Similarly, Solving each equation for and equating the results, we obtain the general law of refraction for waves: But the dihedral angle between two planes is also the angle between their normals. So θ1 is the angle between the normal to the incident wavefront and the normal to the interface, while θ2 is the angle between the normal to the refracted wavefront and the normal to the interface; and Eq.() tells us that the sines of these angles are in the same ratio as the respective velocities. This result has the form of "Snell's law", except that we have not yet said that the ratio of velocities is constant, nor identified θ1 and θ2 with the angles of incidence and refraction (called θ and θt above). However, if we now suppose that the properties of the media are isotropic (independent