page_title: Total internal reflection
section_title: Optical description
hierarchical_section_title: Total internal reflection / Optical description
caption_attribution_description: Magyar: Teljes fényvisszaverődés English: Total internal reflection Deutsch: Totalreflexion
context_page_description: Total internal reflection is the optical phenomenon in which the surface of the water in a fish-tank when viewed from below the water level, reflects the underwater scene like a mirror, with no loss of brightness. In general, TIR occurs when waves in one medium reach the boundary with another medium at a sufficiently slanting angle, provided that the second medium is transparent to the waves and allows them to travel faster than in the first medium. TIR occurs not only with electromagnetic waves such as light and microwaves, but also with other types of waves, including sound and water waves. In the case of a narrow train of waves, such as a laser beam, we tend to describe the reflection in terms of "rays" rather than waves. In a medium whose properties are independent of direction, such as air, water, or glass, each "ray" is perpendicular to the associated wavefronts.
  Refraction is generally accompanied by partial reflection. When waves are refracted from a medium of lower propagation speed to a medium of higher propagation speed, the angle of refraction is greater than the angle of incidence.
context_section_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 thence 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 θᵢ and the angle of refraction θₜ (where t is for transmitted, reserving r for reflected). As θᵢ 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. As θᵢ 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  θᵢ < θc, the incident ray is split, being partly reflected and partly refracted;
  If  θᵢ > θc, the incident ray suffers total internal reflection (TIR); none of it is transmitted.
caption: Fig. 3: Total internal reflection of light in a semicircular acrylic block.
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