Difference between dispersive medium and non-dispersive medium.

In summary, the conversation is about the difference between dispersive and non-dispersive medium, and how to reduce the relation ω=\sqrt{\frac{4β}{m}}sin\frac{Ka}{2} to a non-dispersive form. The expert explains that in a dispersive medium, the phase velocity is not constant and depends on the wave vector, while in a non-dispersive medium it is constant. The expert also clarifies that the equation ω=vsk is valid for both cases. The person requesting help also thanks the expert and encourages them to visit the solid state portion at least once a week.
  • #1
shayaan_musta
209
2
Hello experts!

I have 2 questions.

1)Difference between dispersive and non-dispersive medium.

2)ω=[itex]\sqrt{\frac{4β}{m}}[/itex]sin[itex]\frac{Ka}{2}[/itex] is a relation for dispersive medium. How to reduce it to non-dispersive relation? Here is some math work I have performed to reduce it to non-dispersive relation i.e.

At low frequency K→0
so,
sin([itex]\frac{Ka}{2}[/itex])→[itex]\frac{Ka}{2}[/itex]
so the equation becomes,
ω=[itex]\frac{2}{a}[/itex]νs[itex]\frac{Ka}{2}[/itex]
or,
ω=νsK
where, νs is phase velocity.

So ω=νsK is the relation for non-dispersive medium? Is it?

Thanks in advance.
 
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  • #2
shayaan_musta said:
Hello experts!

I have 2 questions.

1)Difference between dispersive and non-dispersive medium.

2)ω=[itex]\sqrt{\frac{4β}{m}}[/itex]sin[itex]\frac{Ka}{2}[/itex] is a relation for dispersive medium. How to reduce it to non-dispersive relation? Here is some math work I have performed to reduce it to non-dispersive relation i.e.

At low frequency K→0
so,
sin([itex]\frac{Ka}{2}[/itex])→[itex]\frac{Ka}{2}[/itex]
so the equation becomes,
ω=[itex]\frac{2}{a}[/itex]νs[itex]\frac{Ka}{2}[/itex]
or,
ω=νsK
where, νs is phase velocity.

So ω=νsK is the relation for non-dispersive medium? Is it?

Thanks in advance.
Don't know what are β and m in your equations, however, for every frequency ω you can write that ω is equal to phase velocity multiplied wave vector modulus k, only that in a dispersive medium the phase velocity is not constant but depends on k (or ω, depending on which is your independent variable):

νs(k) = [itex]\frac{ω(k)}{k}[/itex]

Group velocity (if of interest) is instead the derivative: νg(k) = [itex]\frac{dω(k)}{dk}[/itex].
 
  • #3
Late reply.

But you are the only one up till now who replied me. So thanks for reply.

β is spring constant. It is come from the derivation of 1D mono-atomic.

m is the mass of the atoms.

You mean ω=vsk is not for the non-dispersive medium?
 
  • #4
shayaan_musta said:
Late reply.

But you are the only one up till now who replied me. So thanks for reply.

β is spring constant. It is come from the derivation of 1D mono-atomic.

m is the mass of the atoms.

You mean ω=vsk is not for the non-dispersive medium?
ω=vsk is valid in both cases. If the medium is non-dispersive, vs is a constant, independent of k; if it's dispersive, vs depends on k.
 
  • #5
Oh great
Thanks a lot.

Best answer.
Thanks.

And one thing I want to say you that kindly, visit this solid state portion at least once a week but try it every week. Because only you are here to answer the post. No one else.

Thanks once again.
 

1. What is the definition of a dispersive medium?

A dispersive medium is a material in which the speed of light or other electromagnetic radiation varies with its wavelength. This means that different wavelengths of light will travel through the medium at different speeds, causing the light to spread out or disperse.

2. How is a non-dispersive medium different from a dispersive medium?

A non-dispersive medium is a material in which the speed of light or other electromagnetic radiation does not vary with its wavelength. This means that all wavelengths of light will travel through the medium at the same speed, without any spreading or dispersion.

3. What are some examples of dispersive and non-dispersive media?

Some examples of dispersive media include glass, water, and air. These materials cause light to spread out and create a rainbow effect. Non-dispersive media include vacuum, air, and some types of glass or plastic that have been carefully engineered to maintain a constant refractive index.

4. How does dispersion affect the behavior of light in a dispersive medium?

The process of dispersion causes different wavelengths of light to travel at different speeds through a dispersive medium. This can lead to changes in the direction of the light, as well as the separation of different colors or wavelengths.

5. What are some practical applications of dispersive and non-dispersive media?

Dispersive media are commonly used in devices such as prisms, diffraction gratings, and optical fibers to manipulate and separate different wavelengths of light. Non-dispersive media are often used in lenses and other optical components to maintain a consistent and predictable behavior of light.

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