# Apparent speed of light in transparent medium

• bakshi
In summary: The result is intuitive, if a wave slows down, its energy is compressed in space and you would expect the amplitude to increase. In summary, the fact that light has a smaller apparent speed in a transparent medium can be explained 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).

#### 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?

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).

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

Claude.

## 1. What is the apparent speed of light in a transparent medium?

The apparent speed of light in a transparent medium is the speed at which light appears to travel through the medium. This is different from the speed of light in a vacuum, which is a constant value of approximately 299,792,458 meters per second.

## 2. How does the apparent speed of light in a transparent medium differ from the speed of light in a vacuum?

The apparent speed of light in a transparent medium is slower than the speed of light in a vacuum. This is because light is constantly being absorbed and re-emitted by the particles in the medium, causing it to appear to travel at a slower rate.

## 3. What factors affect the apparent speed of light in a transparent medium?

The apparent speed of light in a transparent medium is affected by the density, composition, and temperature of the medium. Generally, the denser the medium, the slower the apparent speed of light. Different materials also have different levels of light absorption and scattering, which can affect the apparent speed of light.

## 4. Why is the apparent speed of light important in scientific research?

The apparent speed of light in a transparent medium is important in scientific research because it helps us understand how light interacts with different materials. This can have implications for fields such as optics, materials science, and astronomy.

## 5. How is the apparent speed of light in a transparent medium measured?

The apparent speed of light in a transparent medium is measured using various techniques, such as measuring the time it takes for light to travel through the medium or using instruments that can detect changes in the speed of light as it passes through different materials. These measurements can then be compared to the speed of light in a vacuum to determine the apparent speed of light in the medium.