Relationship between index of refraction and frequency

[Deepa100]

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Here is a quote from the TPR material
"The index of refraction of any material (besides vacuum) varies slightly with the frequency of light: the higher the frequency, the greater the index of refraction. Since red light has a lower frequency than violet, its index of refraction will be lower. Since the index for red light is lower (that is, closer to the index of air), a beam of red light will bend less sharply when it enters the material."

What relationship between the index of refraction and the frequency of light that passes thr' it are they referring to here?

 

[justpremed]

from what i remember of physics...i think this refers to diffraction...single and double slit; if you have white light passing through either a single or double slit apparatus, it'll be split into its respective components, and since red has the lowest index of refraction, it will remain closer to the slit than violet, which will have a greater angle of refraction

i'm not sure if this is what the book is referring to...i have yet to see a problem like this in any of my mcat stuff, though, so unless the book is referring to something completely different, i wouldn't worry too much about it

 

[chemnerd31]

Actually this has to do with dispersion. This is how a prisim is able to make a rainbow out of white light. Since the red light sees a lower index of refraction it is bent less and purple sees a greater index of refraction and is bent more. This happens for all possible wavelengths of light and thus they are spread apart.

 

[tweaked17]

Actually this has to do with dispersion. This is how a prisim is able to make a rainbow out of white light. Since the red light sees a lower index of refraction it is bent less and purple sees a greater index of refraction and is bent more. This happens for all possible wavelengths of light and thus they are spread apart.

Yup, but to add to that, isn't the principle the opposite with diffraction? Red light will wind up on the outside, ie. bent more, with diffraction.

With dispersion red (low freq/larger wavelength) is bent the least, which is why it's the color at the top of the spectrum (closest to the normal) when you split light with a prism.

 

[unsung]

It has to do with chromatic dispersion. Higher frequency light experiences a bigger n, so it bends more sharply than lower freq light. This is why prisms work.

Let's say we have light traveling through glass (n1) before it meets air (n2 = 1 < n2).

From Snell's law, we have n1sin(theta-init) = n2sin(theta-final). Also, we know that n1 = c/v1, and n2 = c/v2.

Longer wavelength = bigger lambda; since speed of light through the medium v = (lambda)(f), bigger lambda = bigger v = faster speed through medium.

So, for our light traveling through glass example, if our light has a longer wavelength, it's going to have a bigger v1, which means it's going to have a smaller n1. Plugging that into Snell's eq, we see that a smaller n1 means a bigger theta-init. (This is from that critical angle eq.)

(I think a key pt in this is realizing that freq of the light is a constant across different mediums, whereas, wavelength can change, which is why bigger wavelength is bigger speed. So, when the problem talks about freqs, just convert that to thinking about wavelengths, and operate on that basis.)

Also, try reading through this:
http://forums.studentdoctor.net/showthread.php?t=508206&highlight=chromatic+dispersion

I had kind of the same Q a while back, but since figured out the freq = constant across different mediums idea.

 

[TawMus]

It has to do with chromatic dispersion. Higher frequency light experiences a bigger n, so it bends more sharply than lower freq light. This is why prisms work.

Let's say we have light traveling through glass (n1) before it meets air (n2 = 1 < n2).

From Snell's law, we have n1sin(theta-init) = n2sin(theta-final). Also, we know that n1 = c/v1, and n2 = c/v2.

Longer wavelength = bigger lambda; since speed of light through the medium v = (lambda)(f), bigger lambda = bigger v = faster speed through medium.

So, for our light traveling through glass example, if our light has a longer wavelength, it's going to have a bigger v1, which means it's going to have a smaller n1. Plugging that into Snell's eq, we see that a smaller n1 means a bigger theta-init. (This is from that critical angle eq.)

(I think a key pt in this realizing that freq of the light is a constant whatever medium it's in, whereas, wavelength can change, which is why bigger wavelength is bigger speed.)

Also, try reading through this:
http://forums.studentdoctor.net/showthread.php?t=508206&highlight=chromatic+dispersion

So that's just off the top of my head. Hope it makes sense. I'll have to think about this some more...

Great explanation, just wanna add one point. Dont forget that Dispersion is an exception(In a vacuum, all frequencies travel at the same speed). For all other cases, the speed of a wave is determined by the medium, not the frequency. Also, I'm pretty sure that speed has to do frequency in this case, not wavelength. Larger frequency = smaller wavelength and vice versa. As the wave passes thru the medium, the wavelength will stay the same(change in wavelength will end up changing the color), what will affect the velocity will be the frequency at which the wave travels at.

 

[TawMus]

Just to clarify, refraction index means how much speed of light is reduced in a medium. n=c/v = c/lamda x f so the shorter the wavelength (blue light) the greater the index of refraction, hence the more reduction in speed.

To sum it up, all frequencies travel at the same speed in one medium UNLESS it is a dispersive medium.

In a dispersive medium, different frequencies(and thus wavelength) will travel at slightly different speeds because of slightly different index of refractions. Hope this helps. 👍

 

[spo01]

I took an ambien an hour ago so I will do my best to explain this!

Ok this is how I remembered this stuff and I've never forgot it. Examkrackers states "longer wavelengths (lower frequencies) move faster through a medium than shorter wavelenghts (higher frequencies), and therefore bend less dramatically at the media interface."
Here are the two visuals I used:
1st visual: (now really visualize this in your head lol) Picture light moving through a prism (we are dealing with chomatic dispersion here). Ok, we have red light that has loooooong wavelength and is very linear like in its appearance. As this red light wave passes through the prism it has no problems passing through the prism and moves through it with high velocity no problems and comes out the other side with only a very little bit bent. Now violet light wants to give this a try and the violet light enters the prism but guess what, she has a high frequency (shorter wavelenghts) which creates more problems because she can't simply pass through as 'smoothly' as red light and thus moves much more slowly through it (makes sense, plug this into n=c/v below and you'll see the lower the 'v' the higher the 'n' thus the more it bends). As a result she really bends when she enters the prism.
plug all this in n=c/v (remember n is always greater than one). and you will have no problem understanding it from there.

Second visual Picture a skateboard coming in at an angle towards the corner of a wall. The front right tire of the skatboard hits the corner first and the wheel locks for a moment and now the skatboard is going in a new direction (a different angle). Point being: the more energy ('speed' for lack of better word) the skateboard has when it hits that interface, the more bending there is. Just like light going into a new medium. The higher energied higher frequency light is going to bend more. The direction in which the axels turn is the direction in which light will bend.