Refraction index vs. wavelength?

[jaejoon89]

How does the refraction index vary with wavelength?

For example, if you take light that initially has just one wavelength and disperse it through a prism and calculate the different indices for each wavelength. I'm guessing they'll be different... Is it linear? exponential? etc.

 

[horatio89]

I'm not sure of the exact physics defining the relationship between the refractive index and the wavelength, but there is an empirical formula relating these two variables known as Cauchy's Formula:

n = A + B/(lambda)^2, where A and B are constants, n is the refractive index at wavelength, lambda.

 

[thomate1]

The refraction index, also known as the refractive index, is a measure of how much light bends when passing through a material. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. The refraction index can vary with wavelength, as different wavelengths of light interact differently with the material. This phenomenon is known as dispersion.

When light is dispersed through a prism, the different wavelengths of light are separated and each wavelength has a different refractive index. This is because the speed of light in a material is dependent on the material's properties, such as its density and composition. As a result, the refractive index for each wavelength will be different.

The relationship between the refractive index and wavelength is not linear, but rather follows Snell's law of refraction. This law states that the angle of refraction is directly proportional to the refractive index and inversely proportional to the wavelength. Therefore, as the wavelength decreases, the refractive index increases.

In some materials, such as glass, the refractive index may vary exponentially with wavelength. This is due to the material's structure and how it affects the speed of light for different wavelengths. In other materials, the refractive index may vary in a more complex manner.

In conclusion, the refraction index varies with wavelength and is not a constant value. It is dependent on the material's properties and follows a non-linear relationship with wavelength. The study of how the refractive index varies with wavelength is important in understanding how light interacts with different materials and can have practical applications in fields such as optics and spectroscopy.