N=c/v=λ0/λ (T doesn't change) and v of light is constant

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Discussion Overview

The discussion centers around the index of refraction (n) as defined by the formula n=c/v and its implications regarding the constancy of light speed in different media. Participants explore the relationship between the index of refraction, wavelength, and the concept of dispersion, questioning whether the index is truly constant across all wavelengths in a given medium.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants assert that the formula n=c/v indicates that the index of refraction is constant for all light in a specific medium.
  • Others question this assertion by highlighting that dispersion suggests the index of refraction varies with wavelength, leading to potential contradictions.
  • One participant notes that the phase velocity of light in a material is dependent on wavelength.
  • Further inquiries are made about whether different wavelengths, such as x-rays and radio waves, travel at different speeds in glass, with some participants affirming that even within visible light, different colors (e.g., violet and red) have different speeds in glass.

Areas of Agreement / Disagreement

Participants express disagreement regarding the constancy of the index of refraction across different wavelengths, with some asserting it is constant in a medium while others argue it varies due to dispersion effects.

Contextual Notes

The discussion highlights the complexity of the relationship between the index of refraction, wavelength, and the behavior of light in different media, with unresolved questions about the implications of dispersion and the definitions involved.

brainyman89
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n=c/v=λ0/λ (T doesn't change) and v of light is constant in a specific medium(i.e. the ratio is constant in given mediums), so the index of refraction is constant for all light when changing mediums.

If we say that index of refraction differs according to the wavelength, then there is contradiction with the above formula n=c/v that says n is constant in specific medium
 
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what i meant to ask is that the formula n=c/v shows that the index is constant for all light and depends only on the medium. however while explaining the dispersion, they say that the index of refraction depends on the wavelength of every light.

isn't there a contradiction?

thanks for answering
 


The phase velocity of the material, v, is dependent upon the wavelength.
 


Born2bwire said:
The phase velocity of the material, v, is dependent upon the wavelength.

do u mean that the velocity of light in a specific medium is not constant and differs according to the wavelength?

for example do x-rays and radio waves have different speeds in glass?
 


brainyman89 said:
do u mean that the velocity of light in a specific medium is not constant and differs according to the wavelength?

for example do x-rays and radio waves have different speeds in glass?
Yes. You don't even need to go that extreme; violet and red wavelengths have different speeds in glass.

Here is a graph of n vs. λ for several different types of glass: visible wavelengths are shown by the pink band:

dispersion-curve3.png
 

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