Dispersion and refractive indices

[user3]

If different frequencies of light have different refractive indices for the same material and travel at different speed in the same material, isn't it inaccurate to say that the speed of light through a certain material is c/n, where n is the "standard" refractive index?

 

[Meir Achuz]

Yes, but it is usually a reasonable approximation.
The dependence of n on frequency is why the 'group velocity' differs from the 'wave velocity'.
A short wave packet would tend to spread because of this depedence of n on frequency.

 

[DrDu]

Well, if there is dispersion, you would rather say that $c(\omega)=c_0/n(\omega)$. Often, people take it for granted that c and n are functions of $\omega$ and don't mention it explicitly.

 

[sophiecentaur]

If different frequencies of light have different refractive indices for the same material and travel at different speed in the same material, isn't it inaccurate to say that the speed of light through a certain material is c/n, where n is the "standard" refractive index?

"n" is specified at a certain wavelength. Visible light covers an octave of frequencies so it is hardly surprising that it interacts with transparent substances differently over that range.

 

[sardar]

Dispersion and refractive indices are important concepts in the study of light and its interaction with materials. The refractive index of a material is a measure of how much the speed of light is reduced when it passes through that material. It is typically denoted by the symbol n and is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the material (v). This means that the speed of light in a material is given by v = c/n.

While it is true that different frequencies of light can have different refractive indices for the same material, this does not invalidate the statement that the speed of light through a certain material is given by v = c/n. This is because the value of n used in this equation is the "standard" refractive index, which is a constant value for a given material at a specific wavelength of light.

The reason why different frequencies of light can have different refractive indices for the same material is due to a phenomenon called dispersion. Dispersion occurs because the speed of light in a material is dependent on its wavelength. This means that light with a shorter wavelength (such as blue light) will have a higher refractive index than light with a longer wavelength (such as red light).

So, while it may seem inaccurate to say that the speed of light through a certain material is c/n, it is actually a simplified representation of a more complex phenomenon. In reality, the speed of light in a material is dependent on both its refractive index and the wavelength of light being used. However, for practical purposes, using the "standard" refractive index is a useful and accurate way to calculate the speed of light in a material.