Apparent speed of light in transparent medium

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Discussion Overview

The discussion revolves around the apparent speed of light in a transparent medium, exploring classical explanations involving the behavior of electrons in response to an oscillating electric field. Participants examine the implications of this behavior on the amplitude of the resultant electric field and the phase relationship between the emitted and driving fields.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants explain that the apparent speed of light in a medium can be understood by considering the motion of electrons in the medium, which emit an electric field that lags behind the source field.
  • There is a claim that the superposition of the source wave and the medium wave results in a total field that has a greater amplitude than the source wave, which raises questions about the physical implications of this increase.
  • One participant asserts that while the amplitude can increase, the net energy remains unchanged, as it is distributed between the electric and magnetic fields and the polarization of the medium's atoms.
  • Questions are raised regarding the assertion that the emitted field is 90 degrees out of phase with the driving field, prompting further clarification about the phase relationship based on the harmonic oscillator model of atoms.
  • Another participant suggests that if a wave slows down, it intuitively follows that its energy would be compressed in space, leading to an increase in amplitude.

Areas of Agreement / Disagreement

Participants express differing views on the implications of amplitude changes and the phase relationship of emitted fields, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

The discussion involves assumptions about the behavior of electrons in oscillating fields and the nature of energy distribution in electromagnetic waves, which may not be fully resolved or universally accepted among participants.

bakshi
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The fact that light has a smaller apparent speed in a transparent medium can be explained classically by considering the motion of the electrons of the medium in the oscillating (radiation) electric field produced by the source. Because they accelerate, these electrons emit an electric field that is 90 degrees out of phase (lagging) with the field produced by the source at the detection point. The total field at the detection point could then be written as a superposition of a cosine wave (source) and a sine wave (medium) having different amplitudes (the medium wave having a smaller amplitude). As expected, the superposition wave is out of phase (lagging) the cosine wave from the source, explaining the smaller apparent speed of light in the medium.

However, the amplitude of this superposition wave is GREATER than the amplitude of the cosine wave, which does not sound right. Putting a transparent medium between the source and the detection point obviously cannot increase the amplitude, right?
 
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bakshi said:
The fact that light has a smaller apparent speed in a transparent medium can be explained classically by considering the motion of the electrons of the medium in the oscillating (radiation) electric field produced by the source. Because they accelerate, these electrons emit an electric field that is 90 degrees out of phase (lagging) with the field produced by the source at the detection point. The total field at the detection point could then be written as a superposition of a cosine wave (source) and a sine wave (medium) having different amplitudes (the medium wave having a smaller amplitude). As expected, the superposition wave is out of phase (lagging) the cosine wave from the source, explaining the smaller apparent speed of light in the medium.

However, the amplitude of this superposition wave is GREATER than the amplitude of the cosine wave, which does not sound right. Putting a transparent medium between the source and the detection point obviously cannot increase the amplitude, right?

Yes it can. What it cannot do is increase the net energy- that resides in
both the electric and magentic fields, and in the polarization (induced
vibrations) of the atoms of the matter.
 
Why do you say the emitted field is 90 degrees out of phase with the driving field?

Claude.
 
Claude Bile said:
Why do you say the emitted field is 90 degrees out of phase with the driving field?

Claude.

If we treat each atom in the medium as a harmonic oscillator, then it can be shown that the position of an electron within that atom will vary in phase with the electric field. It can also be shown that a plane of charges that are moving together produces an electric field equal to a constant times the speed of those charges. If position varies cosinusoidally (in phase with the field), then speed varies sinusoidally. The emitted field (sine) is thus 90 degrees out of phase with the driving field (cosine).
 
Last edited:
The result is intuitive, if a wave slows down, its energy is compressed in space and you would expect the amplitude to increase.

Claude.
 

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