Relationship between wavelength and refraction

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Discussion Overview

The discussion revolves around the relationship between wavelength and refraction, particularly how different wavelengths of light affect the angle of refraction when passing through mediums like water. Participants explore theoretical and practical aspects of this relationship, including the application of Snell's law and concepts of dispersion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant shares experimental results showing varying angles of refraction for different wavelengths of laser light (405 nm, 550 nm, 650 nm) passing through water, questioning how to relate these observations to the index of refraction.
  • Another participant suggests that the refractive index can be expressed as the ratio of the speed of light in vacuum to the speed in the medium, and also as the ratio of wavelengths in vacuum and medium.
  • Some participants mention that the relationship between refractive index and wavelength is complex and material-dependent, involving concepts like dispersion and resonant frequencies.
  • Several participants reference the Sellmeier equation as a potential tool for calculating refractive indices for specific wavelengths, while noting its limitations and the need for material-specific coefficients.
  • Questions arise about the accuracy of angle measurements in the participant's experiments and the apparatus used for such precision.
  • There is a request for information on obtaining refractive indices for materials at various wavelengths, particularly for applications involving thin films.
  • One participant expresses curiosity about the use of specific units for refractive index, while another seeks coefficients for a specific material (CuS).

Areas of Agreement / Disagreement

Participants generally agree that there is a relationship between wavelength and refraction, but multiple competing views exist regarding the complexity of this relationship and the methods to quantify it. The discussion remains unresolved with respect to a definitive formula or approach.

Contextual Notes

Limitations include the dependence on specific material properties, the complexity of dispersion, and the need for precise coefficients for accurate calculations. The applicability of the Sellmeier equation is noted to be limited to certain wavelength ranges.

Who May Find This Useful

This discussion may be useful for individuals interested in optics, experimental physics, and material science, particularly those exploring the effects of wavelength on refraction and related calculations for thin films.

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While playing around with some laser diodes I have at home ~(405, 550, 650 nm) I have noticed that the refracted angles through some mediums (all?) is different.

That is, if I fire my 405nm laser through some water at \theta_{1}=80°, the angle of refraction is ~\theta_{2}=47.01±0.05°.

Now, if I fire my 550nm laser through the same water, at \theta_{1}, the angle of refraction is ~\theta_{3}=47.30±0.05°.

And, finally, if I fire my 650nm laser through the same water, at \theta_{1}, the angle of refraction is ~\theta_{4}=47.50±0.05°.

So, basically, all I know about refraction is snells law: n_{1}/n_{2}=Sin\theta_{2}/Sin\theta_{1}. I don't really know how to mathematically find the relationship between wavelength and refraction.

I googled a bit and didn't see anything that popped out immediately to me. Aside from v=c/n => n = c/v => n = c/(fλ), and that what I'm dealing with here may be "dispersion."

So, is there a relationship here? Is there a relatively simple way for me to relate the angle refracted, wavelength, and the index of refraction of a medium?

How would I predict the angle refracted through a medium at a specific wavelength of light? Is it possible with such little information?

Could I say n = c/(λf) where c and f are fixed (what value do I use for frequency? Or is this specified on my diode?)
(My physics experienced ended with 2nd year physics, and we didn't spend too much time of refraction or optics.)
 
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Drakkith said:
Does this help?
http://en.wikipedia.org/wiki/Refractive_index

I've been there before, and actually http://en.wikipedia.org/wiki/Dispersion_(optics ) is more helpful.

Both do have sections on what I'm asking about, but I wasn't able to construct a relationship that would or show the values I am measuring based on the information there and in other places. That's why I'm here!
 
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In a large tank experiment, water waves are generated with straight, parallel wave fronts, 2 m apart. The wave fronts pass through two openings 5 m apart in a long board. the end of the tank is 3 m beyond the board. Where would you stand, ralative to the perpendicular bisector of the line between the openings, if you want to receive little or no wave action?
 
How on Earth did you measure those angles in the water to that accuracy??
 
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I reiterate:

Is there a way for me to relate the angle refracted, wavelength, and the index of refraction of a medium?

How would I predict the angle refracted through a medium at a specific wavelength of light?

Anyone have any ideas?
 
You need to know that refractive index = speed in vacuum(air)/speed in medium
which can be written ref index = wavelength in vacuum(air)/ wavelength in medium
 
The way that index of refraction depends on frequency is very complicated and material dependent. There is not a single simple equation to describe it. It has to do with resonant frequencies of the material which depends on the material's atomic composition as well as lattice structure. The effect is called dispersion. A simple model for dispersion is the http://faculty.uml.edu/cbaird/95.658%282012%29/Lecture2.pdf.
 
Hey, I looked at this page cause i was looking up
Question: why wavelength of the incident wave changes the angle of bending observed as water waves in a ripple tank travel from deep to shallow water?
and this looks related.
Please & Thank you =]
 
  • #10
truesearch said:
How on Earth did you measure those angles in the water to that accuracy??

I have the same question. What apparatus did you use to obtain those angular measurements?
 
  • #11
The dependence of the angle of refraction on wavelength is a material property. Just like stiffness, or other material properties you need to look them up. If you really want to get into numerical material science simulations, you can, but you should look that info up for your material of concern in a handbook.
 
  • #12
I have the same question, how could I get refractive indices of a material for a set of wavelength? what a relation between then so it leads to calculate n for each lambda. Because I want to measure thin film thickness and it depends on table of a set of (n and lambda). Any information could help.
 
  • #13
  • #14
  • #15
I have another question, can we use (ps/km nm) as a refractive index unit?
 
  • #17
791980 said:
I think this link is more benefit to find n for each lambda for any material. http://www.calctool.org/CALC/phys/optics/sellmeier. it just depends on the sellmeier coefficients.
I would be more careful in using that link as a reference to calculate refractive indices, this is because Sellmeier equation is typically accurate only within certain wavelength range and this range depends on the material. Sellmeier equation doesn't describe the behavior of refractive index for any arbitrary wavelength, and that link doesn't seem to specify the range of validity of Sellmeier equation. The 2nd link shared in post #13 is more reliable.
 
  • #18
We can use this link (in post # 16) with lambda in the range of (1-2 um) and I think its enough for n.
 
  • #19
Can anyone help me finding sellmeier coefficients for CuS? I searched but no result.
I need many n with many lambda, to measure CuS thin film thickness.
 
  • #22
I need to calculate the wavelength of light knowing the refractive index but not using frequency. Can anyone help me?
 
  • #23
I don't think so. Unless you give more context.
 

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