Red and Violet speed inside a prism?

[Francium87]

When light travel to a denser medium, the velocity decreases by the medium's refractive index

so when comparing a violet light travelling from air to water to red light also traveling from air to water...their speed in water would be decreased by n because their wavelengths (not freq.) was reduced by n. Therefore both lights would travel at the same speed in water. ok

when examining a white light shining on a prism, would u say the the speed of the violet color is the same as red color inside the prism? if so that means the red light would exit prism before the violet light, because it takes a shorter path and time (fraction of seconds that our eyes can't see) compare to violet light?

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[milski]

The velocities for different wavelengths in a certain media are almost, almost the same but not exactly the same. Most of the time you can ignore that difference and treat say what you've said above - that light travels at the same speed in water, etc.

With that said, there is a minimal difference which leads to the prism effect that you bring up later. The reason that white light gets split in different colors by the prism due to the velocities not being exactly the same.

I don't have any number handy but my gut feeling is that the difference in speeds is insignificant compared to the difference in path lengths and the red light will exit first.

 

[Francium87]

hmm so the difference in their velocities increases in prism and our eyes can actually detect this difference by seeing different color....now, the time the light spends inside a prism is dependent on the pathway it takes as well as its frequency? I'm thinking that since violet light has a higher frequency therfore it will cause more excitation and therefore more time till the emitted light is released, which is again insignificantly detected macroscopically

 

[MD Odyssey]

hmm so the difference in their velocities increases in prism and our eyes can actually detect this difference by seeing different color....now, the time the light spends inside a prism is dependent on the pathway it takes as well as its frequency? I'm thinking that since violet light has a higher frequency therfore it will cause more excitation and therefore more time till the emitted light is released, which is again insignificantly detected macroscopically

This is a commonly misunderstood topic. Indeed, I wrote a post a long time ago here discussing frequency and was totally wrong about it then. Let me correct that now.

The frequency of a wave is a constant and never changes in different media because it is determined entirely by the source. Everything else changes. The frequency stays the same, but the wave length changes. There is also a corresponding change in the wave speed as well. Keep this fact in your mind because the MCAT will test whether you know it or not.

 

[Francium87]

yah the frequency never changes when traveling between mediums (easy to remember from the half thick-half thin rope oscillating at the same freq.) but the difference in frequencies among the colors changes when travelling between different medium.

 

[MD Odyssey]

hmm so the difference in their velocities increases in prism and our eyes can actually detect this difference by seeing different color.

This is somewhat incorrect.

The prism effect is due to a couple of factors. First, and the one you should understand for the MCAT, is expressed by Snell's law.

You can see that the refractive and incident angles are related to each other by the ratios of the indices of refraction. The reason that a prism creates a continuous spectrum from white light is because the index of refraction is slightly dependent upon the frequency. This is what you should really understand. It's true that the index of refraction is equal to the ratio of the speed of light in a vacuum to its speed in the medium, but that wouldn't explain the spreading of the beam.

A second factor, probably not important for the MCAT, but interesting, is that prisms are cut to amplify the effect. The classic example is this:

By cutting the glass this way, the beam of light gets spread twice - once when it hits the interface on the left and a second time when it hits the interface on the right. This second splitting increases the separation and makes the effect appear more significant.

Also, just to be complete, this phenomenon of the speed of a wave being dependent upon its frequency is referred to as dispersion. The prism is usually used as an example of dispersive medium and, while true, is a rather convoluted way to explain the effect you see because it doesn't explain why the light leaves at different angles.

 

[milski]

yah the frequency never changes when traveling between mediums (easy to remember from the half thick-half thin rope oscillating at the same freq.) but the difference in frequencies among the colors changes when travelling between different medium.

If the frequencies never change, the differences between them never change either.

What MD Odyssey has written is perfect and should get you through the MCAT.

MD Odyssey, why do you say that the differences in velocities don't explain the spread? The indexes of refraction are proportional to velocity change at the interface. Assuming same velocities in the initial media will lead to slightly different velocities in the second media, slightly different refraction index for each frequency and slightly different refraction angles, creating the spread.

 

[MD Odyssey]

MD Odyssey, why do you say that the differences in velocities don't explain the spread? The indexes of refraction are proportional to velocity change at the interface.

I think what bothers me is the fact that the argument of varying speeds doesn't account for the refraction angle.

An argument based on differences in speeds can be made, but it requires invoking Fermat's law, which is a rather subtle application. The MCAT doesn't require that type of understanding - Fermat's law is a very subtle thing and not easy to jive with what most premeds are normally aware of.

Hope this helps.

 

[Francium87]

Thanks MD Odyssey and milski
you guys been great in explaining this concept, I had to think about it yesterday while walking back to my car lol

milski I don't know why I said the difference in frquencies changes, f=v/wavelength has to be constant since Energy has to be conserve (E=hf) f has to be constant

 

[milski]

I think what bothers me is the fact that the argument of varying speeds doesn't account for the refraction angle.

An argument based on differences in speeds can be made, but it requires invoking Fermat's law, which is a rather subtle application. The MCAT doesn't require that type of understanding - Fermat's law is a very subtle thing and not easy to jive with what most premeds are normally aware of.

Hope this helps.

Ah, you mean in the context of MCAT, that certainly makes sense.