# Reversibility, Principle of

## Reversibility, Principle of

a basic principle of geometric optics that postulates the reversibility of the path of light rays. According to the principle of reversibility, the path of an elementary light flux that propagates through the series of optical media 1, 2, 3, … along the ray ABCD … AB, BC, CD, and so on being the segments of the ray within the media 1, 2, 3, …, respectively) is replaced by the opposite path … DCBA if the light emanates from a point of the ray in the direction opposite to the original direction. The principle of reversibility is widely used, particularly in the design of optical systems and in the construction of the optical images produced by such systems.

In its simplest interpretation the principle of reversibility is a corollary of Snell’s law of the refraction of light. This law applies to any two adjacent media of the series 1, 2, 3, …: sin i1/sin i2 = n2/n1 = n12. Here n122 is the relative refractive index and equals the ratio of the absolute refractive indices n2 and n1 of the second and first media, respectively, i1 is the angle of incidence of the light ray on the interface between the two media, and i2i is the angle of refraction in the second medium. If i1 is substituted for i2, and i2 for i1, their values remain unchanged, since n1 and n2 are invariant. An analogous statement is valid for reflection of light; thus the principle of reversibility can be applied to any optical system— to both lens systems and mirror systems.

The principle of reversibility presupposes that the attenuation of a light ray during its passage through an optical medium because of reflection, refraction, and absorption is not affected by a reversal of the direction of the ray. This follows from the reversibility of the Fresnel equations with respect to the direction of light rays. The principle of reversibility can be extended to systems that consist of media having a continuously variable refractive index. In media that are characterized by optical anisotropy—whether natural or owing to external factors—the problem of the validity of the principle of reversibility is considerably more complex. The situation is also quite complicated for light fluxes of high intensity, such as laser radiation.

### 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.
Sliusarev, G. G. O vozmozhnom i newzmozhnom v optike, 3rd ed. Moscow, 1960.
Clark, J. R. “On Reversibility and Irreversibility in Optics.” Journal of the Optical Society of America, 1953, vol. 43, no. 2.
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