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23 Aug 2005, 14:05
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#1
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Registered User
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Location: South Pacific
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Snell's law and isotropic materials
I have been puzzling over a little problem I have. If a ray of light is travelling from one material (a) to another (b) then given that we know the angle in (a) one calculates the refracted angles using snell's law - easy enough. but for an anisotropic material, the refractive index is a function of angle. now in the case where the ray is travelling from an anisotropic material to isotropic, it is easy to work out the angle in the isotropic (just the old snell's law again) but if a ray is travelling from isotropic to anisotropic, or even anisotropic to anisotropic, then I am at a loss as to how to calculate the angle in material (b)
anyone got any ideas how to do this?
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Last edited by Radical Edward; 24 Aug 2005 at 13:42.
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23 Aug 2005, 15:51
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#2
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Destroyer of Worlds
Join Date: Feb 2002
Posts: 552
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Re: Snell's law and isotropic materials
Don't you have all your 'an's in the wrong places?
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23 Aug 2005, 15:54
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#3
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Destroyer of Worlds
Join Date: Feb 2002
Posts: 552
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Re: Snell's law and isotropic materials
When you say you 'know the angle' of the ray in material (a), at which point are you measuring the angle? At the point it reaches the boundary?
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“In spite of the roaring of the young lions at the Union, and the screaming of the rabbits in the home of the vivisect, in spite of Keble College, and the tramways, and the sporting prints, Oxford still remains the most beautiful thing in England, and nowhere else are life and art so exquisitely blended, so perfectly made one.”
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24 Aug 2005, 13:41
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#4
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Registered User
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Re: Snell's law and isotropic materials
Quote:
Originally Posted by Jennifer
Don't you have all your 'an's in the wrong places?
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oops. I'll swap them all round.
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I think it's time we blow this scene, get everybody and the stuff together..........
ok 3..... 2..... 1.. let's jam
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24 Aug 2005, 13:43
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#5
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Registered User
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Re: Snell's law and isotropic materials
Quote:
Originally Posted by Jennifer
When you say you 'know the angle' of the ray in material (a), at which point are you measuring the angle? At the point it reaches the boundary?
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yeap.
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I think it's time we blow this scene, get everybody and the stuff together..........
ok 3..... 2..... 1.. let's jam
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24 Aug 2005, 13:44
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#6
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Registered User
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Re: Snell's law and isotropic materials
to all the people who negrepped me, I just thought I would say that I posted this on this forum because I know there are clever people like Jennifer and MrL who might have an idea as to what to do.
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I think it's time we blow this scene, get everybody and the stuff together..........
ok 3..... 2..... 1.. let's jam
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24 Aug 2005, 14:13
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#7
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NEWSBOT
Join Date: Dec 2000
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Re: Snell's law and isotropic materials
thats a fair point, but wouldn't you have been better just sending a pm to those two ?
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24 Aug 2005, 14:20
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#8
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Re: Snell's law and isotropic materials
maybe, but there might be other physicists that I am unaware of, or it might be one of those obscure topics that people spontaneously take an interest in (though I doubt it)
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I think it's time we blow this scene, get everybody and the stuff together..........
ok 3..... 2..... 1.. let's jam
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24 Aug 2005, 22:06
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#9
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Destroyer of Worlds
Join Date: Feb 2002
Posts: 552
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Re: Snell's law and isotropic materials
Do you have an explicit function for the refractive index? You might find it easier to consider wavefronts rather than rays, then there's a whole subject dedicated to it. I never had a particularly strong grasp of non-linear optics, but if you can be more specific about what it is you're trying to do, I might be able to help.
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“In spite of the roaring of the young lions at the Union, and the screaming of the rabbits in the home of the vivisect, in spite of Keble College, and the tramways, and the sporting prints, Oxford still remains the most beautiful thing in England, and nowhere else are life and art so exquisitely blended, so perfectly made one.”
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24 Aug 2005, 22:13
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#10
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Ball
Join Date: Oct 2001
Posts: 4,410
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Re: Snell's law and isotropic materials
Does one have to worry about polarisation or is it just lines and tensors?
If desperate, you could define the full 3D problem using Fermat's principle and solve it numerically. I think a basic 2D problem (where the boundary is aligned with the principal axes of the permittivity tensors) is isomorphic to an isotropic problem by scaling.
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#linux
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25 Aug 2005, 01:28
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#11
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Powering your life...
Join Date: Dec 2004
Location: Dublin
Posts: 400
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Re: Snell's law and isotropic materials
Hmmm.... personally I'd need a bit of help from the advanced amterails physics guys to take a solely mathematical approach- but surely an approach more experimental in nature could lead to a better understanding of the situation?
Now, let's *try* the conceptual approach.
An ansiotropic material has 21 elastic constants while an Isotropic only has 2 of these independant variables- Young's modulus E and the Poisson's ratio v.
I won't list the 21 ansitropic ones [not that i can remember...lol]
These 2 heavily ifluence the stiffness and compliance matrices- ensuring the material properties are independent of direction. And isotropic tends to have a constant refractive index- eg. air.
Ansitropic is where it gets tricky alright.
Ansitropic tends to be split up into 2 categories- uniaxial and biaxial:
Uniaxial- tetragonal and hexagonal crystal systems, generally occurs in crystals and fragile, brittle plastics.
Each wave length that passes through is characterised by 2 extreme refractive indices- this is why a crystal will show so many colours, each wavelength travels at a differant speed and hence the ray gets split up.
Biaxial- triclinic, monoclinic, and orthorhombic crystal systems- This one has 3 extreme refractive indexes with the 2nd be the exacy intermediate of the two.
So that was actually all relevant- :-p
What should happen is that each wavelength is dispersed and then undergoes refraction and each ray takes a differant path and needs to be calculated sepreately- which is where the advanced materials physichists come in!
Hope it has been of some help- i'm a bit drunk so didn't exactly offer the clearest of posts to aid you!
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25 Aug 2005, 01:30
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#12
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Powering your life...
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Re: Snell's law and isotropic materials
PLease forgive grammar+speeling, again I'm a little drunk, apologies.
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25 Aug 2005, 02:00
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#13
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I dunno...
Join Date: Jun 2003
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Re: Snell's law and isotropic materials
Goodness, this is all a tad confusing.
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27 Aug 2005, 03:00
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#14
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Friendly geek of GD :-/
Join Date: Nov 2000
Location: On my metal roid
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Re: Snell's law and isotropic materials
Quote:
Originally Posted by Radical Edward
maybe, but there might be other physicists that I am unaware of, or it might be one of those obscure topics that people spontaneously take an interest in (though I doubt it)
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I'm a physics-wannabe failing maths right now, but doing ok in physics because of a "solid feeling" ;-)
1st year at uni is almost over now.
Reading this thread could've made me more clever!
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[ »] Entropy increases! :-/
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