Phase and signal velocity of light inside a medium

In summary, The conversation discusses the relationship between light's phase velocity and signal's velocity in a linear medium with refractive index n, as well as the arrival time of photons from a laser inside the medium. It also mentions the group velocity and dispersion relation for light traveling through glass, and provides a link to a website with technical information on glass properties. The conversation concludes with an agreement on the relationship between signal velocity and group velocity for common glasses in the visible range.
  • #1
lightarrow
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Don't know if this is the correct forum.

While we know that light's phase velocity in a linear medium with refration index n is c/n, what can we say about signal's velocity? If I switch on a laser inside the medium (let's say glass) at t = 0, when will the first photon arrive to a detector placed L metres away? At t = L/(c/n) or at t = L/c or else?
 
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  • #2
If n does not vary too rapidly with wavelength, a pulse of light will travel with the group velocity [tex]v_g=\frac{\partial\omega}{\partial k}[/tex].
 
  • #3
clem said:
If n does not vary too rapidly with wavelength, a pulse of light will travel with the group velocity [tex]v_g=\frac{\partial\omega}{\partial k}[/tex].
Do you know the dispersion relation [tex]\omega(k)[/tex] or [tex]n(\lambda)[/tex] in the visible range for a common glass?
 
  • #4
This depends a bit on the kind of glass you have.

Have a look at the download page of Schott glasses (a rather large company dealing with glasses and optical filters):

http://www.schott.com/advanced_optics/english/tools_downloads/download/index.html#Catalogues and Datasheets [Broken]

Techical information 29 has some basic definitions and shows refraction index versus wavelength for fused silica glass. In the top of the page there is also a link to a glass map leading to an overview of some commonly used glasses, where n versus wavelength is given for 20 or so standard wavelengths for each filter. Maybe look for BK7. This is also a very common glass.
 
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  • #5
Cthugha said:
This depends a bit on the kind of glass you have.

Have a look at the download page of Schott glasses (a rather large company dealing with glasses and optical filters):

http://www.schott.com/advanced_optics/english/tools_downloads/download/index.html#Catalogues and Datasheets [Broken]

Techical information 29 has some basic definitions and shows refraction index versus wavelength for fused silica glass. In the top of the page there is also a link to a glass map leading to an overview of some commonly used glasses, where n versus wavelength is given for 20 or so standard wavelengths for each filter. Maybe look for BK7. This is also a very common glass.
Thanks for the interesting link.
So, you agree that signal velocity = group velocity for common glasses in the visible range?
 
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  • #6
lightarrow said:
So, you agree that signal velocity = group velocity for common glasses in the visible range?
Yes.
 
  • #7
clem said:
Yes.
Thanks to both (but you are the same person?)
 

1. What is the difference between phase velocity and signal velocity of light inside a medium?

The phase velocity of light refers to the speed at which the phase of an electromagnetic wave travels through the medium. This does not necessarily represent the actual speed of the light itself. The signal velocity, on the other hand, is the speed at which information or energy is transmitted through the medium by the light wave. This is typically slower than the phase velocity, as it takes into account factors such as absorption and re-emission of light by the particles in the medium.

2. How does the refractive index of a medium affect the phase and signal velocity of light?

The refractive index of a medium is directly related to the phase and signal velocity of light. The higher the refractive index, the slower the phase velocity of light will be. This is because the particles in the medium cause the light to bend and travel a longer path. The signal velocity also decreases with a higher refractive index, as the light must travel through more particles and undergo more interactions, slowing down the transmission of information.

3. Does the wavelength of light affect the phase and signal velocity in a medium?

Yes, the wavelength of light does impact the phase and signal velocity in a medium. Generally, shorter wavelengths have higher phase velocities, while longer wavelengths have lower phase velocities. This is due to the relationship between wavelength and frequency, where shorter wavelengths have higher frequencies and therefore a higher phase velocity. The signal velocity, however, is not directly affected by the wavelength of light.

4. Can the phase and signal velocity of light in a medium be manipulated?

Yes, the phase and signal velocity of light in a medium can be manipulated through various methods. One way is by changing the properties of the medium, such as the refractive index or density, which affects the speed of the light. Another way is by using special materials, such as metamaterials, which have unique properties that can be engineered to control the phase and signal velocity of light. Additionally, external factors such as temperature, pressure, and electric fields can also influence the velocity of light in a medium.

5. How does the phase and signal velocity of light in a medium relate to the speed of light in a vacuum?

The phase and signal velocity of light in a medium are always less than the speed of light in a vacuum, which is approximately 299,792,458 meters per second. This is because light travels slower when interacting with particles in a medium, causing a decrease in both the phase and signal velocity. However, the speed of light in a vacuum is considered to be the maximum possible speed, and the phase and signal velocities in a medium can never exceed this speed.

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