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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 34, Iss. 4 — Apr. 1, 1944
  • pp: 222–228

Optics InfoBase > JOSA > Volume 34 > Issue 4 > Impact of a Wave Packet and an Absorbing Particle

Impact of a Wave Packet and an Absorbing Particle

HERBERT E. IVES  »View Author Affiliations

JOSA, Vol. 34, Issue 4, pp. 222-228 (1944)

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HERBERT E. IVES, "Impact of a Wave Packet and an Absorbing Particle," J. Opt. Soc. Am. 34, 222-228 (1944)

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  1. H. E. Ives, J. Opt. Soc. Am. 33, 163–166 (1943).
  2. Note that we have incidentally derived, from non-relativistic considerations (for this particular problem), the Einstein formula for the composition of velocities, for if [equation]. Equation (14) derived below has in fact been derived elsewhere [Becker, Theorie der Electricität (Teubner, Leipzig, 1933), Vol. 2, p. 348] by assuming that the atoms in the absorbing body move so that their velocities conform to the Einstein formula.
  3. Strictly speaking it is the kinetic energy when the particle is brought to rest, but since we have postulated that w0 is the value of velocity when the particle is brought to rest without escape of heat, this value of kinetic energy also applies to the particle in motion.
  4. Abraham, Theorie der Elekirizität (B. G. Teubner, Leipzig, 1905), Vol. 2, p. 383, Eq. (245).
  5. This value for the pressure on a moving absorbing target was obtained by the writer in a previous paper [H. E. Ives, J. Opt. Soc. Am. 32, 32 (1942), in which pertinent references are given] but without the detailed analysis provided by the present paper.
  6. There is also involved in this analysis (in evaluating the energy density from the source at the target) the convention that the distance between source and target is always measured at the target, on a scale attached to the source and experiencing the Fitzgerald contraction proper to the velocity of the source.
  7. Since, as pointed out by Epstein [Am. J. Phys. 10, 1 (1942)] the Fitzgerald contraction has been derived from a simple law of attraction, and the variation of clock rate with velocity follows from the variation of mass with velocity, there appears to be no need of a principle of relativity to derive the general invariance of optical phenomena with motion.

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