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

In summary, the refractive index of a material changes with the wavelength of light due to changes in the speed of light when entering a medium. This is known as light dispersion and can be seen in the visible range where the index increases for shorter wavelengths and decreases for longer wavelengths. This property is specific to each material and can be further understood by looking up "light dispersion" or "Cauchy's dispersion formula". This change in refractive index also results in attenuation of the light, which is explained by the Kramers-Kronig Dispersion relations and the concept of causality.
  • #1
pras_quantum
15
0
can some one tell me how the refractive index changes with the wave length of the light?
 
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  • #2
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?
 
  • #3
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).
 
  • #4
You can get more information by googling "Cauchys dispersion formula".
 
  • #5
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.
 

1. What is refractive index?

Refractive index is a measure of how much light is bent or refracted when passing through a medium, such as a substance or material.

2. How is refractive index calculated?

Refractive index is calculated by dividing the speed of light in a vacuum by the speed of light in the medium. This gives a ratio that represents the bending of the light.

3. What factors affect refractive index?

The refractive index of a substance is affected by its density, temperature, and chemical composition. It can also vary depending on the wavelength of the light passing through it.

4. Why is refractive index important?

Refractive index is important in many scientific fields, including optics, material science, and chemistry. It helps to understand how light behaves and interacts with different substances, and can also be used to identify and characterize materials.

5. How is refractive index used in practical applications?

Refractive index is used in a variety of practical applications, such as designing lenses for glasses and cameras, determining the purity of substances, and analyzing the composition of materials. It is also used in industries such as pharmaceuticals, where it can help to ensure the quality and consistency of products.

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