Reflection of light from a uniformly moving mirror

American Journal of Physics

Volumn 72, Issue 10, 2004, Pages 1316-1324

  Gjurchinovski, Aleksandar ^a  

^a SS CYRIL AND METHODIUS UNIVERSITY   (Macedonia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7444246099     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1778390     Document Type: Article

References (20)

1. For a beautiful historical overview and a good introductory account of the problem of reflection and refraction of electromagnetic waves from moving boundaries, see B. M. Bolotovskii and S. N. Stolyarov, "Wave reflection from a moving mirror and related problems," Usp. Fiz. Nauk 159, 155-180 (1989).
2. A. Einstein, "Zur Elektrodynamik bewegter Körper," Ann. Phys. (Leipzig) 17, 891-921 (1905); reprinted in Einstein's Miraculous Year: Five Papers That Changed the Face of Physics, edited by John Stachel (Princeton U.P., Princeton, 1998).
3. A. Einstein, "Zur Elektrodynamik bewegter Körper," Ann. Phys. (Leipzig) 17, 891-921 (1905); reprinted in Einstein's Miraculous Year: Five Papers That Changed the Face of Physics, edited by John Stachel (Princeton U.P., Princeton, 1998).
4. See, for example, M. Born and E. Wolf, Principles of Optics (Cambridge U.P., Cambridge, 1999), 7th ed.
5. G. P. Sastry and T. R. Ravury, "Modeling some two-dimensional relativistic phenomena using an educational interactive graphics software," Am. J. Phys. 58, 1066-1073 (1990).
6. C. Møller, The Theory of Relativity (Clarendon, Oxford, 1972), 2nd ed.
7. See, for example, E. Hecht, Optics (Addison-Wesley, Reading, MA, 1987), 2nd ed.
8. A word of caution! The visual appearance of a high-velocity moving object (that is, the process of seeing) and the measurement of its shape (that is, the process of relativistic measurement) are completely different. See, for example, J. Terrel, "Invisibility of the Lorentz contraction," Phys. Rev. 116, 1041-1045 (1959), and M. L. Boas, "Apparent shape of large objects at relativistic speeds," Am. J. Phys. 29, 283-286 (1961).
9. A word of caution! The visual appearance of a high-velocity moving object (that is, the process of seeing) and the measurement of its shape (that is, the process of relativistic measurement) are completely different. See, for example, J. Terrel, "Invisibility of the Lorentz contraction," Phys. Rev. 116, 1041-1045 (1959), and M. L. Boas, "Apparent shape of large objects at relativistic speeds," Am. J. Phys. 29, 283-286 (1961).
10. An illustrative example of this misconception is the discussion associated with Fig. 15-3 in R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading. MA, 1989). Vol. 1, p. 15-6. See in particular, part (c) of the caption, which states "Illustration of the diagonal path taken by the light beam in a moving 'light clock.' "
11. The result follows from the requirement that the phase of a plane-polarized electromagnetic wave must be an invariant quantity under a Lorentz transformation. See, for example, Sec. 2.9 in Ref. 5 and J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., Sec. 11.3(d).
12. It is worth noticing that Eq. (14) also can be obtained by a direct application of the addition law for relativistic velocities. See, for example, L. Landau and E. Lifshitz, The Classical Theory of Fields (Addison-Wesley, Cambridge, 1951). Still another way to derive the aberration formula is discussed in Ref. 9.
13. The statement that the lateral dimensions of a uniformly moving object remain unchanged with respect to the lateral dimensions of the same object at rest can be easily proved by using only Einstein's first postulate. See, for example, Problem 6.1 in A. A. Pinsky, Problems in Physics (MIR, Moscow, 1988).
14. For a more detailed discussion on the length of a moving object, the process of measurement, and Lorentz contraction in special relativity, see T. A. Moore, Six Ideas That Shaped Physics, Unit R: The Laws of Physics Are Frame-Independent (WCB/McGraw-Hill, Boston, 1998).
15. The physical length of a uniformly moving object would equal the object's proper length, that is, the object's length measured in the reference frame in which the object is at rest.
16. The statement that Lorentz contraction of a plane mirror in uniform rectilinear motion implies Lorentz contraction of any uniformly moving object can be clarified by imagining the object's surface to consist of an infinite number of infinitely small plane mirrors having different inclination angles with respect to the object's motion.
17. R. A. Schumacher, "Special relativity and the Michelson-Morley interferometer," Am. J. Phys. 62, 609-612 (1994).
18. A. A. Michelson and E. W. Morley, "On the relative motion of the earth and the luminiferous ether," Am. J. Sci. 34, 333-345 (1887).
19. E. H. Kennard and D. E. Richmond, "On reflection from a moving mirror and the Michelson-Morley experiment," Phys. Rev. 19, 572-577 (1922).
20. R. S. Shankland, "Michelson-Morley experiment," Am. J. Phys. 32. 16-35 (1964).