wave is absorbed by a lossy external medium ("attenuated total reflectance"), or diverted by the outer boundary of the external medium or by objects embedded in that medium ("frustrated" TIR). Unlike partial reflection between transparent media, total internal reflection is accompanied by a non-trivial phase shift (not just zero or 180°) for each component of polarization (perpendicular or parallel to the plane of incidence), and the shifts vary with the angle of incidence. The explanation of this effect by Augustin-Jean Fresnel, in 1823, added to the evidence in favor of the wave theory of light. The phase shifts are utilized by Fresnel's invention, the Fresnel rhomb, to modify polarization. The efficiency of the total internal reflection is exploited by optical fibers (used in telecommunications cables and in image-forming fiberscopes), and by reflective prisms, such as image-erecting Porro/roof prisms for monoculars and binoculars. Optical description Although total internal reflection can occur with any kind of wave that can be said to have oblique incidence, including (e.g.) microwaves and sound waves, it is most familiar in the case of light waves. Total internal reflection of light can be demonstrated using a semicircular-cylindrical block of common glass or acrylic glass. In Fig.3, a "ray box" projects a narrow beam of light (a "ray") radially inward. The semicircular cross-section of the glass allows the incoming ray to remain perpendicular to the curved portion of the air/glass surface, and then hence to continue in a straight line towards the flat part of the surface, although its angle with the flat part varies. Where the ray meets the flat glass-to-air interface, the angle between the ray and the normal (perpendicular) to the interface is called the angle of incidence. If this angle is sufficiently small, the ray is partly reflected but mostly transmitted, and the transmitted portion is refracted away from the normal, so that the angle of refraction (between the refracted ray and the normal to the interface) is greater than the angle of incidence. For the moment, let us call the angle of incidence θ and the angle of refraction θt (where t is for transmitted, reserving r for reflected). As θ increases and approaches a certain "critical angle", denoted by θc (or sometimes θcr), the angle of refraction approaches 90° (that is, the refracted ray approaches a tangent to the interface), and the refracted ray becomes fainter while the reflected ray becomes brighter.