The Difference in Refraction Angles of Different Colored Light

[HeavyMetal]

As I understand it, when you beam white light through a glass prism, light disperses and refracts. Red light refracts the least and violet light refracts the most. I am dying to know: why do different frequencies of light have different angles of refraction? Specifically, why is it that an increase in frequency corresponds to an increase in the refractive index?

I was guessing that this is a result of interaction with the medium. As red light has the least relativistic momentum, it would lose the most energy. This would translate into a smaller angle of refraction. Violet light, being much higher in energy, would be affected the least, and therefore would exhibit a greater angle of refraction.

Thoughts?

 

[Vanadium 50]

It's best not to guess.

Did you read the Wikipedia article? http://en.wikipedia.org/wiki/Dispersion_(optics)

If so, is something unclear?

 

[HeavyMetal]

I couldn't find anything when I searched for the answer. I appreciate the link.

However, I'd argue that guessing is a good exercise to work your creative problem solving skills. Even if you're wrong, you found your own answer and worked at it on your own. Is there something wrong with that?

 

[davenn]

I couldn't find anything when I searched for the answer. I appreciate the link.

However, I'd argue that guessing is a good exercise to work your creative problem solving skills. Even if you're wrong, you found your own answer and worked at it on your own. Is there something wrong with that?

But the guess is no good to you if it gives you the wrong answer

Science is worked out by putting foreward a mathematical theory and then testing that theory with repeated experiments and logging the results. If the theory doesn't quite match the observed results, then the theory may need adjusting

Dave

 

[HeavyMetal]

I agree! It's no good if you're wrong! But I'm happy to have made the effort. Sometimes you need to take risks to gain a conceptual understanding of things. I have friends who just look things up without attempting a solution and their conceptual understanding is crap.

It seems as though I was at least half right with my attempt at a solution though. What I was describing was angular dispersion, and it does in fact have to deal with the interaction of the light with the medium. I had guessed absorbance (and concomitant reemission) played a role too. Still wondering if relativistic momentum plays a role.

"Because of the Kramers–Kronig relations, the wavelength dependence of the real part of the refractive index is related to the material absorption, described by the imaginary part of the refractive index (also called the extinction coefficient)." - en.m.wikipedia.org/wiki/Dispersion_(optics)

 

[Chronos]

Monochromatic light does not suffer color separation upon passing through a prism. 'White' light does because it is a combination of different wavelengths that are bent differently upon passing through a prism.

 

[DrDu]

I was guessing that this is a result of interaction with the medium. As red light has the least relativistic momentum, it would lose the most energy. This would translate into a smaller angle of refraction. Violet light, being much higher in energy, would be affected the least, and therefore would exhibit a greater angle of refraction.

The guess in the first sentence is true, but the rest not. Typical material like water or glass will absorb light in the ultraviolet part of the spectrum. However, they will also interact with light whose frequency is above or below this frequency. This is analogous to a driven harmonic oscillator, who will react the more to a external perturbation the closer the frequency is to it's resonance frequency.
That means violet light interacts stronger with the medium than red light. Part of the energy of the light wave will be converted into electronic excitation energy (polarization) of the medium. However, this electronic excitations are localized on the molecules and don't move. Hence the light is slowed down and the wavelength in the medium is shorter.

 

[HeavyMetal]

Thank you, high schoolphys, for all of your support. I am happy you backed me up and explained my exact learning style!

The guess in the first sentence is true, but the rest not. Typical material like water or glass will absorb light in the ultraviolet part of the spectrum. However, they will also interact with light whose frequency is above or below this frequency. This is analogous to a driven harmonic oscillator, who will react the more to a external perturbation the closer the frequency is to it's resonance frequency.
That means violet light interacts stronger with the medium than red light. Part of the energy of the light wave will be converted into electronic excitation energy (polarization) of the medium. However, this electronic excitations are localized on the molecules and don't move. Hence the light is slowed down and the wavelength in the medium is shorter.

This is invaluable information to me. So what you're telling me is that the phonon of the material that the prism is made of is resonating at a frequency more similar to violet light than red light, and that as a result the violet light is more strongly perturbed? And that we can deduce, because red to violet exhibits an increasing angle of refraction, that the absorbance of this material is of higher frequency than violet?

In this experiment, do people generally use glass or quartz? I know that glass absorbs UV light and that quartz transmits it.

Thanks in advance :)

 

[DrDu]

In this experiment, do people generally use glass or quartz? I know that glass absorbs UV light and that quartz transmits it.

Thanks in advance :)

Quartz also absorbs in the UV, although at higher frequencies than the absorption lines of normal glass.
Materials also absorb in the IR part of the spectrum, although this is due to molecular vibrations and not electronic absorption. Generally, the refractive index rises both below and above an absorption line (normal refraction ) but falls in the region of the absorption line (anomalous refraction).

 

[HeavyMetal]

Quartz also absorbs in the UV, although at higher frequencies than the absorption lines of normal glass.

Materials also absorb in the IR part of the spectrum, although this is due to molecular vibrations and not electronic absorption. Generally, the refractive index rises both below and above an absorption line (normal refraction ) but falls in the region of the absorption line (anomalous refraction).

Awesome! Is this perturbation due to the phonon of the material?

 

[DrDu]

Awesome! Is this perturbation due to the phonon of the material?

Yes, phonons are the quanta of vibrations in solids.

 

[jtbell]

Posts about educational philosophy and PF policy on "guessing" have been split off into a separate thread:

https://www.physicsforums.com/showthread.php?t=763297