Why do red light waves bend less when passing through a prism?

[Infrasound]

When passing through a prism, why are red light waves bent the least. I understand that red light waves have a longer wavelength. This alone does not explain why they bend less.

In looking at diagrams of huygens principle, it is clear that a wavefront will bend, but why would one wavelength bend more than another?

 

[Meir Achuz]

The index of refraction in glass depends on the wavelength, and is smaller for red light than blue, so red bends less.

 

[Infrasound]

I think that I stated that above. Refraction depends on wavelength. The question is WHY does the index of refraction depend on wavelength.

It is my understanding that the speed of light should be the same for all wavelengths in both mediums. The differences in index of refraction would make sense if different wavelengths of light move at different speeds through the prism, but all wavelengths move at the same rate, I think.

Do all wavelengths move at the same rate through the prism?

 

[Meir Achuz]

Different wavelengths of light DO move at different speeds through the prism. n depends on epsilon which depends on frequency.

 

[Infrasound]

Thanks, I did check into that after my last post, and found it to indeed be true. I think the next problem would be finding out why light of different wavelengths moves at different speeds through glass.

 

[AJ Bentley]

Whoa - slow down.

You'll get to that - it's to do with dielectric constant and the way EM waves interact with matter. But you won't need to look at it until second year at Uni. You need some heavy duty math under your belt first.
Give yourself a break. Or buy a copy of Feynman's Lectures on Physics.

 

[my_wan]

You can look at it this way:
The refractive index is the ratio of light speed in a vacuum relative to that speed in a medium. The slowing of light in a medium is due to interactions with that medium. Red light has a longer wavelength, and interactions will occur at maximum of once per wavelength, hence the speed (refractive index) is different for different wavelengths in a given medium. This explains the speed variations. The bending is actually an effect of Snell's law, which depends on the change in speed, not the absolute refractive index. For instance consider light passing from glass to water.

 

[AJ Bentley]

Red light has a longer wavelength, and interactions will occur at maximum of once per wavelength, hence the speed (refractive index) is different for different wavelengths in a given medium.

Ooh goosebumps! That's a really good summary.
And since the more wavelengths you get in (highest frequency), the more the interaction and the slower the speed, it follows that blue light is slower than red and bends more.

 

[Infrasound]

So it seems as if there is some reason why the time in between wave maximums affects how quickly they are transmitted from one piece of matter (particle) to the next.

 

[my_wan]

So it seems as if there is some reason why the time in between wave maximums affects how quickly they are transmitted from one piece of matter (particle) to the next.

It doesn't have to effect rate a photon travels between interactions. Only that the interaction itself involves some non-zero time period in which the photon is not traveling.

 

[Born2bwire]

So it seems as if there is some reason why the time in between wave maximums affects how quickly they are transmitted from one piece of matter (particle) to the next.

Generally we can model a bulk material as being a peroidic lattice. For example, let's just take a block of copper, we can microscopically describe it as a series of copper atoms spaced at regular distances. So for this bulk material, the material properties (the material constituents, the lattice spacings, etc) do not change as we change the frequency of the light. What changes is the dimensions (lattice spacing for example) in regards to the wavelength. As light passes through a material, the behavior of the light on a macroscopic level has to satisfy certain boundary conditions. If the "electrical distances" of the properties of the material changes, then the way that the light propagates through the material must change accordingly to satisfy these boundary conditions.

So it is not how "quickly the photons are transmitted." It has to do with how the light interacts with the material and how the constraints that govern these interactions change as the wavelength of the light changes. While I talked about the material in terms of its microscopic properties, these constraints and such are discussed on a more macroscopic level for classical electrodynamics. So we do not talk about photons or absorption rates and so forth. We can use a broader perspective and still achieve the same results.

I should note though that do not think that the increase in the wavelength dictates that the speed will always increase/decrease. my wan's abstraction above may give you the impression that the effects of changing the wavelength will result in a deterministic change in the behavior. The actual changes in speed and propagation are very subtle and we can actually shift the trends in the material. That is, we may notice that the speed of light decreases as we increase the frequency, but all of a sudden at some point the trend may reverse and the speed starts to increase. There are a lot of sutbleties to the problem.

 

[jtbell]

See also post #4 in this thread:

https://www.physicsforums.com/showthread.php?t=104715