Dispersive Medium

[jdla]

---

Members do not see this ad.

In this type of medium, why does the velocity increases with wavelength?

What is the difference between a dispersive and non dispersive medium?

 

[physics junkie]

1.) Why does velocity increase with wavelength in a dispersive medium? That is a very difficult question that I'm not sure anyone here could answer for you...at least in my opinion. If you really want to know ask on physicsforums.com but tell them you don't know much physics or they'll drown you in some explanation that's impossible to understand.

2.) In a dispersive medium the velocity of the wave traveling through the medium is different depends on its wavelength. Another way, what your wavelength is when you hit the medium directly impacts how fast you travel through that medium. In a nondispersive medium all wavelengths are treated equally and all go through the medium at the same speed.

Imagine some material that when blue light was incident on the material that it would go through at 5m/s but when red light was incident it would travel through at 7m/s. That would be a dispersive medium. A nondispersive medium would have to send all wavelengths through at the same velocity.

 

[unsung]

Is it true that in optics, speed of a light wave is dependent on its frequency, and not just on the medium ? This was mentioned in prep class tonight as an exception to the rule that speed of a wave is solely dependent on the medium.. it kind of confused me.

If speed of light is a constant, how does speed of light depend on frequency ?

 

[physics junkie]

Is it true that in optics, speed of a light wave is dependent on its frequency, and not just on the medium ? This was mentioned in prep class tonight as an exception to the rule that speed of a wave is solely dependent on the medium.. it kind of confused me.

If speed of light is a constant, how does speed of light depend on frequency ?

I think your teacher was confused but you'll probably want to ask him/her.

Since the speed of light in a material depends on the refractive index, and the refractive index may depend on the frequency of the light, light at different frequencies can travel at different speeds through the same material. This effect is called dispersion.

is an equation that always holds that links the index of refraction, the speed of light in a vacuum, and the phase velocity.

So that means that the speed of light depending on the frequency means the index of refraction depends on the frequency...and the index of refraction is what's unique to each medium. So this exception is no actual exception. You should ask your teacher about this because it undermines their understanding.

Light always travels at c in a vacuum. That is what people refer to as constant. However, when the medium has an index of refraction that is greater than 1 then the phase velocity(more precise definition than speed...but there are other types of velocities such as the group velocity) in the medium decreases to satisfy the equation above. I can't explain to you how to calculate the index of refraction of a medium but don't worry you don't need to understand that. The speed of light is a constant in the universe and that means a bit more than you probably think it does unless you're familiar with special relativity. Special relativity says no matter how fast you're flying in your spaceship away from a beam of light coming from a flashlight the beam will always look like it's coming at you at the same speed. In all reference frames, both those that are accelerating or traveling at a constant velocity, light in a vacuum will propagate at a speed c.

 

[Kaustikos]

I think your teacher was confused but you'll probably want to ask him/her.

is an equation that always holds that links the index of refraction, the speed of light in a vacuum, and the phase velocity.

So that means that the speed of light depending on the frequency means the index of refraction depends on the frequency...and the index of refraction is what's unique to each medium. So this exception is no actual exception. You should ask your teacher about this because it undermines their understanding.

Light always travels at c in a vacuum. That is what people refer to as constant. However, when the medium has an index of refraction that is greater than 1 then the phase velocity(more precise definition than speed...but there are other types of velocities such as the group velocity) in the medium decreases to satisfy the equation above. I can't explain to you how to calculate the index of refraction of a medium but don't worry you don't need to understand that. The speed of light is a constant in the universe and that means a bit more than you probably think it does unless you're familiar with special relativity. Special relativity says no matter how fast you're flying in your spaceship away from a beam of light coming from a flashlight the beam will always look like it's coming at you at the same speed. In all reference frames, both those that are accelerating or traveling at a constant velocity, light in a vacuum will propagate at a speed c.

So, ceterus parabus, light coming from the sun (vacuum) goes through the atmosphere and is defracted (differing refractive index) and so, depending on the refractive index of the atmosphere (can't remember what it is at the top of my head), would I technically be able to see different colors in a race to the finish? Say that we actually had TWO suns, one was red and one was violet, would I actually be able to see two different rays colliding on an object, "Experimentally"?

 

[unsung]

I think your teacher was confused but you'll probably want to ask him/her.

is an equation that always holds that links the index of refraction, the speed of light in a vacuum, and the phase velocity.

So that means that the speed of light depending on the frequency means the index of refraction depends on the frequency...and the index of refraction is what's unique to each medium. So this exception is no actual exception. You should ask your teacher about this because it undermines their understanding.

So, let me see if I understand this right. Light always travels at c in a vacuum, but in a medium (each medium has a distinct n), the speed of light differs depending on what its frequency is ? I think I'm confused, because then it seems like light would be an exception to the idea that the speed of a wave is dependent only on the medium it propagates through ?

 

[tncekm]

I think your teacher was confused but you'll probably want to ask him/her.

I think what his teacher was alluding to is that high frequency (short wavelength) light rays tend to have a higher energy than those of lower frequency (longer wavelength) which means the light rays with high energy will slow down extremely slightly less as they collide with other molecules than those with less energy. This means that they "will" have slightly different speeds. And this is what allows us to construct a diffraction grating because "technically" the different wavelengths travel at "slightly" different speeds through the mediums and thus have slightly different indices of refraction allowing us to see that nice pretty rainbow 🙂

And, I want to emphaise this point: speed of light in a vacuum is NOT dependent on frequency, but, when its moving through a non-vacuum medium it is very, very slightly. And, this is easy to intuit because high frequency = high energy and low frequency = low energy.

If I didn't make my explanation clear I'll try to repost later.

 

[physics junkie]

Each medium doesn't have a distinct n....each medium has a distinct n for a particular frequency. The factors that go into determining n are the density of the medium(denser mediums increase the chances of absorption and slow down light) and the frequency of light(and therefore its energy) that is traveling through the medium. Typically the refractive index increases with frequency but that's not always the case. It depends on what wavelengths/frequencies that your medium likes to absorb light at...typically shorter wavelengths are absorbed more often but this doesn't have to be the case so its not a rule, just a common pattern.

Can you see how properties of the medium determines everything? It determines what frequencies are absorbed more often and its density determines almost everything else. In fact there is no clear-cut theoretical way to predict the index of refraction so this is an oversimplification.

On the other hand I guess you could say the frequency of light determines how the medium reacts to it--so in that sense its a perspective issue. Still according to the equation n is what determines it's velocity...and n is just an experimentally discovered constant.

 

[physics junkie]

So, ceterus parabus, light coming from the sun (vacuum) goes through the atmosphere and is defracted (differing refractive index) and so, depending on the refractive index of the atmosphere (can't remember what it is at the top of my head), would I technically be able to see different colors in a race to the finish? Say that we actually had TWO suns, one was red and one was violet, would I actually be able to see two different rays colliding on an object, "Experimentally"?

Well, different cones in your eye would be activated than if you just had either sun alone. How your brain would put together that information is not something I could tell ya.

 

[unsung]

Each medium doesn't have a distinct n....each medium has a distinct n for a particular frequency. The factors that go into determining n are the density of the medium(denser mediums increase the chances of absorption and slow down light) and the frequency of light(and therefore its energy) that is traveling through the medium. Typically the refractive index increases with frequency but that's not always the case. It depends on what wavelengths/frequencies that your medium likes to absorb light at...typically shorter wavelengths are absorbed more often but this doesn't have to be the case so its not a rule, just a common pattern.

Can you see how properties of the medium determines everything? It determines what frequencies are absorbed more often and its density determines almost everything else. In fact there is no clear-cut theoretical way to predict the index of refraction so this is an oversimplification.

On the other hand I guess you could say the frequency of light determines how the medium reacts to it--so in that sense its a perspective issue. Still according to the equation n is what determines it's velocity...and n is just an experimentally discovered constant.

Okay, thanks for the explanations, guys. Reading through all that, let me see if I understand this correctly now:

n = c/v = c/(lambda)(f), where c is ALWAYS a constant, f is ALWAYS a constant (freq of light does not change when moving into a new medium), s.t. c/f = (lambda)👎 = some constant.