How does the refractive index change with the wavelength of light?

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Discussion Overview

The discussion centers on how the refractive index of materials changes with the wavelength of light, exploring concepts related to light propagation in different media, dispersion, and the underlying physical principles. The scope includes theoretical aspects and references to specific materials and formulas.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks how the refractive index changes with the wavelength of light.
  • Another participant explains that the speed of light changes in different media, leading to a change in wavelength while frequency remains constant, suggesting that the refractive index is related to these changes.
  • It is noted that in the visible range, the refractive index typically increases as the wavelength decreases, with blue light having a higher index than red light for many common materials.
  • A participant mentions that for some materials, there are ranges where the refractive index increases with increasing wavelength, indicating anomalous dispersion.
  • Reference to Cauchy's dispersion formula is provided for further information on the topic.
  • Another participant connects the dependency of the refractive index on wavelength to material attenuation, referencing the Kramers-Kronig relations and a specific textbook for deeper understanding.

Areas of Agreement / Disagreement

Participants express varying views on the relationship between refractive index and wavelength, with some agreeing on general trends while acknowledging exceptions and specific material behaviors. The discussion remains unresolved regarding the implications of dispersion and attenuation.

Contextual Notes

Participants highlight that the behavior of refractive index can depend on the specific material and spectral range, and mention the need to look up values for particular materials. There are references to complex relationships such as anomalous dispersion and the Kramers-Kronig relations that are not fully explored in the discussion.

Who May Find This Useful

This discussion may be useful for individuals interested in optics, materials science, and physics, particularly those exploring the properties of light in different media and the theoretical underpinnings of dispersion.

pras_quantum
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can some one tell me how the refractive index changes with the wave length of the light?
 
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The speed of light changes when entering some medium other than vacuum. If the frequency of the light (the number of wave cycles entering a surface per unite time) were to change, it would suggest that the boundary of the medium that the light was entering is destroying waves, which a bunch of very important people decided does not happen (in reality (experiment) it doesn't happen).

Since the speed of the light changes (frequency times wavelength), and the frequency doesn't change, then the wavelength must be changing. The speed on light in a vacuum is c, the speed of light in a material is v=c/n. Thus the wavelength must change as λ/n (λ being the wavelength of the light in a vacuum). Does this answer your question?
 
The answer depends on the spectral range and material.
In the visible range the index increases when the wavelength decreases (for many common materials). It's larger for blue light than for red light. The difference is in general small (few percent for glass). It is a property of the material so you have to look up the numbers for the material of interest.
Look up "light dispersion" for specific values.
For some materials there are spectral ranges in which the index of refraction increases when the wavelength increases (anomalous dispersion).
 
You can get more information by googling "Cauchys dispersion formula".
 
If the index of refraction of a material (glass, lucite, etc.) is dependent on the wavelength (or frequency) of light (dispersion), then the material must have attenuation. This is a direct result of the Kramers-Kronig Dispersion relations. See page 311 in Jackson "Classical Electrodynamics" Second Edition. It is useful to read the sections in Jackson on dispersion and causality.
 

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