# What does refractive index depend upon?

1. Sep 7, 2011

### Misr

what does refractive index depend upon?
The answer of my text book is "wavelength" so how,although it cannot be controlled directly??
I thought It depends on the speed of light in the media
I don't understand how to answer these kinds of questions
for example :what does the deviation angle of a prism depends upon?
[PLAIN]http://utopia.cord.org/cm/leot/course06_mod07/Fig3.gif [Broken]
I thought it depends upon three factors which are :1-angle of incidence(theta1).
2-angle A and theta 4
but that's not the right answer , It depends only on theta1 or angle of incidence not the other two angles-despite the fact that we can change angle A

Another thing that is confusing me
"the minimum angle of deviation of a prism depends on the refractive index"
According to the relation
[PLAIN]http://utopia.cord.org/cm/leot/course06_mod07/image87.gif [Broken]
it could depend on other factors
I'm totally confused!

May be the answer to these kind of questions is the factor which can be controlled directly
but in my first question the answer was "wavelength" although we cannot change wave lenth in a direct way

hope you could understand me
Thanks very much

Last edited by a moderator: May 5, 2017
2. Sep 7, 2011

### Staff: Mentor

The refractive index of a material, regardless of its shape, is dependant on the wavelength of the light. It looks like your questions are assuming that the prism isn't changed at all, but the light can be.

3. Sep 7, 2011

### Misr

you didn't answer my questions
Can we control the wavelength by a direct method?
why don't we say that it is dependant on the velocity of light in the medium??
n=c/v

4. Sep 8, 2011

### Curl

If you are going to use that prism how you want it then you must use monochormoatic light. Lasers can put out 1 wavelength, e.g. helium-neon lasers (most popular) will spit 633nm.

Different wavelengths of light travel at different speeds through the material, so since n=c/v then the "refractive index" changes by definition depending on what wavelength you are talking about.

5. Sep 8, 2011

### Staff: Mentor

It would help if you used proper grammar and structure to make your questions clear. I tried very hard to understand what you were asking. I don't even see where you asked if we can control the wavelength unless the 2nd sentence is actually a question.

Anyways, you can change the wavelength of the light that enters the prism by simply using a different color. Is that what you wanted to know?

I believe it is because the refractive index determines the speed in the medium, not the other way around.

6. Sep 8, 2011

### Misr

but how about the frequency???
Yeah.but how would this affect the refractive index if the refractive index=c\v

That's indeed a great answer.This is the kind of answer I need

7. Sep 8, 2011

### Staff: Mentor

It changes when wavelength changes. Do you know what frequency and wavelength represent?

From wikipedia on dispersion: In general, the refractive index is some function of the frequency f of the light, thus n = n(f), or alternatively, with respect to the wave's wavelength n = n(λ). The wavelength dependence of a material's refractive index is usually quantified by an empirical formula, the Cauchy or Sellmeier equations.

I believe that the refractive index will be slightly different for different wavelengths of light. A refraction telescope must use multiple lenses to focus the different wavelengths of light all at the same point. A single lens will have a noticeable distance between the focal points of different colors. The larger the distance between wavelengths, the longer the distance between focal points of the two colors.

8. Sep 8, 2011

### Claude Bile

Refractive index is given as;

$$n = \sqrt{\mu\epsilon}$$

Where $\epsilon$ is the relative permittivity and $\mu$ is the relative permeability of the medium.

Permittivity is related to the electric polarizability, which is the electric dipole moment per unit volume per unit of electric field strength. Similarly, permeability is related to the magnetic polarizability, which is the magnetic dipole moment per unit volume per unit magnetic field strength.

For "ordinary" optical materials, the relative permeability is very close to 1, hence;

$$n = \sqrt{\epsilon}$$

In general, the permittivity is a 3x3 matrix (to account for birefringent materials that have more than one principal refractive index) and each component is dependent on the frequency.

Indeed. It is the induced dipole moment per unit field (electric and magnetic) that ultimately affects the velocity of EM waves through the medium.

Claude.