applies to linear polarization in the s or p direction. The Imbert–Fedorov effect is an analogous effect for circular or elliptical polarization, and produces a shift perpendicular to the plane of incidence. Applications Optical fibers exploit total internal reflection to carry signals over long distances with little attenuation. They are used in telecommunication cables, and in image-forming fiberscopes such as colonoscopes. In the catadioptric Fresnel lens, invented by Augustin-Jean Fresnel for use in lighthouses, the outer prisms use TIR to deflect light from the lamp through a greater angle than would be possible with purely refractive prisms, but with less absorption of light (and less risk of tarnishing) than with conventional mirrors. Other reflecting prisms that use TIR include the following (with some overlap between the categories): Image-erecting prisms for binoculars and spotting scopes include paired 45°-90°-45° Porro prisms (Fig.14), the Porro–Abbe prism, the inline Koenig and Abbe–Koenig prisms, and the compact inline Schmidt–Pechan prism. (The last consists of two components, of which one is a kind of Bauernfeind prism, which requires a reflective coating on one of its two reflecting faces, due to a sub-critical angle of incidence.) These prisms have the additional function of folding the optical path from the objective lens to the prime focus, reducing the overall length for a given primary focal length. A prismatic star diagonal for an astronomical telescope may consist of a single Porro prism (configured for a single reflection, giving a mirror-reversed image) or an Amici roof prism (which gives a non-reversed image). Roof prisms use TIR at two faces meeting at a sharp 90° angle. This category includes the Koenig, Abbe–Koenig, Schmidt–Pechan, and Amici types (already mentioned), and the roof pentaprism used in SLR cameras; the last of these requires a reflective coating on one face. A prismatic corner reflector uses three total internal reflections to reverse the direction of incoming light. The Dove prism gives an inline view with mirror-reversal. Polarizing prisms: Although the Fresnel rhomb, which converts between linear and elliptical polarization, is not birefringent (doubly refractive), there are other kinds of prisms that combine birefringence with TIR in such a way that light of a particular polarization is totally reflected while light of the orthogonal polarization is at least partly transmitted. Examples include the Nicol prism, Glan–Thompson prism, Glan–Foucault prism (or "Foucault prism"), and Glan–Taylor prism. Refractometers, which measure refractive indices, often use the critical angle. Rain