## ABERRATION OF LIGHT IN TERMS OF THE THEORY OF RELATIVITY AS ILLUSTRATED ON A CONE AND A PYRAMID

JOSA, Vol. 9, Issue 3, pp. 223-233 (1924)

http://dx.doi.org/10.1364/JOSA.9.000223

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### Abstract

A ray of light is propagated in the *XY* plane and its angle with the *X*-axis is determined by two observers, *S* and *S*′, who are in relative motion to each other along the *X*-axis at a velocity *q* (expressed as a fraction of the velocity of light). If the angles measured by them are δ and δ′, then it is proved that tan½δ/tan½δ′=cos(45°′½α)/cos(45°-½α), where Sin α=*q*. This relationship is interpreted geometrically by means of a cone in oblique coordinates. The axes of coordinates are *X, Y*, and time *T*. The *T* and *X* axes are different for the two observers, and the four axes *T, X, T*′, *X*′, form a Lorentzian Plane to which Y is perpendicular. The properties of the cone are considered in detail and a mechanical model of the cone, built of wood and iron, is described. At a desired velocity *q*, one can compare directly the angles δ and δ′. It is also shown that the relationship between the angles δ, δ′, and α can be represented on a pyramid. References are made to other articles by the same writer, in which oblique axes are also used for the solution of problems in the theory of relativity.

**Citation**

VLADIMIR KARAPETOFF, "ABERRATION OF LIGHT IN TERMS OF THE THEORY OF RELATIVITY AS ILLUSTRATED ON A CONE AND A PYRAMID," J. Opt. Soc. Am. **9**, 223-233 (1924)

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-9-3-223

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