Optical Path

optical path [′äp·tə·kəl ′path]

(optics)

For a ray of light traveling along a path between two points, the optical path is the integral, over elements of length along the path, of the refractive index. Also known as optical distance; optical length.

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Optical Path 

The optical path between points A and B of a transparent medium is the distance optical radiation, or light, would travel in a vacuum during the time it takes to move from A to B. Since the speed of light in any medium is less than in a vacuum, the optical path is always greater than the distance actually traversed by the light except in the limiting case of a vacuum, where the optical path is equal to the distance traversed.

The trajectory of a light beam in an optical system consisting of ρ homogeneous media is a broken line. In such a system the optical path is equal to [com] Σ^p/_kn_k, where l_k is the distance traveled by the light in the kth medium (k = 1,2,…,p),n_k is the refractive index of the medium, and Σ is the summation sign. For one medium (p = 1), the sum is reduced to a single term l_n. In an optically inhomogeneous medium with a smoothly changing n, the trajectory of a beam is a curve. The optical path in such a medium is [com] ∫_A^Bn(l) dl, where dl is an infinitely small element of the beam trajectory.

The concept of optical path plays a major role in optics, especially geometrical and crystal optics, because it makes possible comparison of the paths traversed by light in media in which the rate of propagation differs. The locus of points for which the optical paths, reckoned from the same source, are identical is called the surface of the light wave; light oscillations on this surface are in the same phase.

REFERENCES

Landsberg, G. S. Optika, 4th ed. Moscow, 1957. (Obshchii kurs fiziki, vol. 3.)
Tudorovskii, A. I. Teoriia opticheskikh priborov, 2nd ed., part 1. Moscow-Leningrad, 1948.
Born, M, and E. Wolf. Osnovy optiki, 2nd ed. Moscow, 1973. (Translated from English.)