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reflecting prism[ri′flek·tiŋ ′priz·əm]
an optical prism such that any optical radiation (light) entering the prism is reflected within it from one or more polished flat surfaces (faces) that bound the prism. If a beam of light rays is incident on a reflecting prism for the surrounding medium and emerges from the prism into the medium in a direction not perpendicular to the corresponding faces, then it is refracted at these faces. Like many other optical prisms, reflecting prisms are often not prisms in the strict geometrical sense. They differ from spectroscopic prisms in that they do not spatially separate the transmitted radiation according to frequencies—that is, they do not produce dispersion of the light. They differ from polarizing prisms in that they are not doubly refracting. Reflecting prisms are for the most part made from optically isotropic materials.
A beam incident on a face of a reflecting prism from the surrounding medium at some angle α returns into the medium from the same or another face and at the same angle; the original direction of the beam may be altered by an angle ω ≠ 0 (see Figure 1). In most cases, the reflection from the surfaces of reflecting prisms is total internal reflection. If the angle of incidence of the beam on a reflecting face is less than the critical angle, a highly reflecting coating of silver or aluminum is applied to the outside of the face. Introducing a reflecting prism into a light beam is optically equivalent to placing in the beam a plane-parallel plate of the same material as the prism and of a thickness equal to the distance traversed by the beam in the prism: when the beam is obliquely incident on the prism, there result the same transverse displacement of the beam and the same aberrations. The aberrations are significant only when working with optical prisms in convergent and divergent beams; if an optical prism is placed in a parallel beam, its aberrations have essentially no effect on image quality. Reflecting prisms for visible light are made of optical glass. Prisms for infrared radiation are made of special types of glass, silicon, germanium, fluorite, lithium fluoride, cesium iodide, and other materials transparent to such
radiation. The materials used in prisms for ultraviolet radiation include quartz, fluorite, and lithium fluoride. The principal types of reflecting prisms are shown in Figure 1.
Reflecting prisms are used to change the direction of a light beam, to reduce the size (length) of an optical system, and to reform an image—for example to rotate the image 180° or obtain a mirror image. The path of rays in a principal section of a reflecting prism obeys the inversion rule: an erect image is produced by a reflecting prism with an even number of reflecting faces, such as a rhomboid prism or a pentagonal prism; a mirror, or inverted, image is produced by a reflecting prism with an odd number of faces, such as a right-angle prism or a Dove prism. This rule does not hold if the rays are reflected in different cross sections; for example, a right-angle roof prism produces an erect image. Indeed, any reflecting prism can be converted to a roof prism by replacing one of its reflecting faces with two faces between which the angle is 90°. Roof reflecting prisms are used to reverse the image from right to left and vice versa. Combinations of several reflecting prisms, such as Porro systems of the first and second kind, are used to accomplish several functions simultaneously—to change the dimensions of the optical system, to change the direction of the light rays, and to invert the image.
L. N. KAPORSKII