# Refractive index and dispersion (name & usage of eq and conceptual questions)

1. Jul 23, 2010

### fysikjatack

Sry for a proper wall of text, and it´s probably pretty "chatty" too, as I reason about things back and forth... Plz do feel free to comment on the reasoning since I post it to learn how to think about these things...

I believe that I have sometime learned that one can relate refractive index n, wavelength $$\lambda$$ and angle of refraction $$\alpha$$ as follows:

n = $$\lambda$$ / sin($$\alpha$$)

This describes dispersion, right? But is there a name to the above stated relation? Is it a simplification or combination of some other eq/s? Maybe this is only a valid approximation for VIS or why is it so hard to find this relation stated?

Refractive index depends on wavelength.

If lambda = 5 and sin(a)=1, then n =5.

If I use another wavelength, say lambda*=10. Can I find the angle of refraction of this light by

sin(a)=10/5 ? Or is n really different for different wavelengths in such a way that one cannot deduce alpha for wavelength1 by knowing alpha for wavelength2?
One cannot use the eq like this since the first calculation only yields n =5 FOR lambda=5, but for lambda=10 n is something different?

Refractive indices are different for different wavelengths, then that means that longer wavelengths are not slowed down as much as short wavelengths upon entering a new medium? (in some cases the opposite I guess..)

Snell's law operates with ratio of n1/n2? Different wavelengths will experience different refractive indices, but all wavelengths always travel n1/n2 times faster(or slower) in medium 1 compared to itself in medium 2, is this correct? (coming to think of it - it isnt,right?)
That is all wavelengths are slowed down by the same factor upon entering a new medium? But all wavelengths travel at c in vacuum and if they are slowed down by the same factor they would have same speed and hence same refractive indices? This does not make sense, does it?

Or does Snell's law deal with one wavelength at a time as n1 and n2 (and the ratio of n1/n2) is different for different wavelengths? The ratio n1/n2 is not necessarily the same for different wavelengths..? Hence, different wavelengths will also have different ratios of sines of angle of incidence and angle of refraction?
I.e. n2/n1=sin(theta1)/sin(theta2) also varies with wavelength..? Then it makes sense that red and blue light with same angle of incidence will have different angle of refraction - dispersion! This must be the case - n1/n2 is NOT constant for different wavelengths, right?

When one look up refractive indices in tables they must actually be specified for a certain wavelength..?

Lights of different wavelengths have different energy and momentum, could one say that because of this they have to be slowed down differently in a medium (have different refractive indnidces) to fulfil som/e law/s of conservation or something?

Why are some materials more "dispersive" than others?
Are materials with higher optical density always more dispersive than materials with lower optical density? (maybe they are less dispersive, the point is, is "dispersivity" proportional to refractive index?)

Obviously, I´m a bit confused about this. Maybe I just mix this up with diffraction stuff and itself...

2. Jul 25, 2010

### fysikjatack

I´m trying to make it a bit more readable and sum it up;
I found some information in other threads and other sites, but would like to be assured that I understand it correctly and some of the desired information is yet to be found.

Are the statements 1 through 3 correct or false? Can you answer questions 4 through 8?

1.When one look up refractive indices in tables they must actually be specified for a certain wavelength..?

2. If you use n = $$\lambda$$/sin($$\alpha$$), you cannot use the calculated value of n for another set of lambda & sin(a) as the calculated n is only valid for the lambda used to calculate it in the first place.

3. In Snell´s law n1/n2 = sin2(a)/sin1(a), the ratio of n1/n2 will be different for different wavelengths. That is, n1/n2 must be given separately for each wavelength of which one wishes to find the angle of refraction of. (Assuming known angle of incidence).

4. What is the relation n = $$\lambda$$/sin($$\alpha$$) called? I saw someone writing this and assumed it was about disperion, could it be that I mix it up with something about diffraction where one usually writes: d sin(a) = $$\lambda$$or d = $$\lambda$$/sin($$\alpha$$) for minimum intensity(where d is width of slit, $$\alpha$$ is angle and $$\lambda$$is wavelength). Or d sin($$\alpha$$) = n $$\lambda$$for the n:th. Maybe the person who wrote the eq mixed it up and got n = $$\lambda$$/sin(a) out of this, or is n = $$\lambda$$/sin($$\alpha$$) an actual equation?
I do more and more suspect that it was miswritten/misinterpreted/misread as it isnt that easy to find online and I just realized that it might make the units strange to have: refractive index = wavelength / sin(angle) ...

And am I interpreting it correctly? Is it a simplification/combination/approximation for VIS?

5. Why are some materials more "dispersive" than others? Is "dispersivity" somehow proportional/related to refractive index?

6. Why do light of different wavelengths experience different refractive indices? Different wavelengths mean different energy and momentum, is this something about conservation?

7. Are there any exact equations for dn/d(lambda)? I´ve seen curves and it does not seem likely that its always a certain % of energy/momentum change and not an absolute value (more or less analougos to work function of photons). Or am I wrong here, could any of these be the case?

8. If you know that a material has refractive index 1.5 for 550 nm light, can you somehow deduce the refractive index of this material for 750 nm light?