Apparent speed of light in transparent medium

[bakshi]

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?

 

[Antiphon]

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.

 

[Claude Bile]

Why do you say the emitted field is 90 degrees out of phase with the driving field?

Claude.

 

[bakshi]

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).

 

[Claude Bile]

The result is intuitive, if a wave slows down, its energy is compressed in space and you would expect the amplitude to increase.

Claude.