page_title: Total internal reflection
hierarchical_section_title: Total internal reflection
caption_attribution_description: A 405nm violet diode laser is gently focused to a thin beam withh a large depth of focus. It enters a thick glass plate at one clear-cut edge. The angle of incidence is chosen for total internal reflection within the glass. The laser beam travels zig zag and makes the glass fluoresce greenish. This fluorescence light is emitted in all directions and therefore can be seen from the outside.
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: Total internal reflection (TIR) is the optical phenomenon in which the surface of the water in a fish-tank (for example) when viewed from below the water level, reflects the underwater scene like a mirror, with no loss of brightness (Fig. 1). In general, TIR occurs when waves in one medium reach the boundary with another medium at a sufficiently slanting angle, provided that the second ("external") medium is transparent to the waves and allows them to travel faster than in the first ("internal") 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 (Fig. 2), 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 (e.g., from water to air), the angle of refraction (between the refracted ray and the line perpendicular to the refracting surface) is greater than the angle of incidence (between the incident ray and the perpendicular). As the angle of incidence approaches a certain limit, called the critical angle, the angle of refraction approaches 90°, at which the refracted ray becomes parallel to the surface. As the angle of incidence increases beyond the critical angle, the conditions of refraction can no longer be satisfied; so there is no refracted ray, and the partial reflection becomes total. For visible light, the critical angle is about 49° for incidence at the water-to-air boundary, and about 42° for incidence at the common glass-to-air boundary.
  Details of the mechanism of TIR give rise to more subtle phenomena. While total reflection, by definition, involves no continuing flow of power across the interface between the two media, the external medium carries a so-called evanescent wave, which travels along the interface with an amplitude that falls off exponentially with distance from the interface. The "total" reflection is indeed total if the external medium is lossless (perfectly transparent), continuous, and of infinite extent, but can be conspicuously less than total if the evanescent 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 reflection is exploited by optical fibers (used in telecommunications cables and in image-forming fiberscopes), and by reflective prisms, such as erecting prisms for binoculars.
caption: Fig. 2: Repeated total internal reflection of a 405 nm laser beam between the front and back surfaces of a glass pane. The color of the laser light itself is deep violet; but its wavelength is short enough to cause fluorescence in the glass, which re-radiates greenish light in all directions, rendering the zigzag beam visible.
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