# Speed of light in unusual materials

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1. Jul 27, 2014

### skate_nerd

Hi all,

I've recently learned some details about refractive indices in different media that I never knew about before. Up until now, I was aware that the speed light travels in a certain medium is dependent on the wavelength of light used. However I wasn't aware that for different kinds of materials, the dependence on wavelength can be higher or lower. For example: (this is what brought up the curiosity in me) when switching from 532 nm light to 1064 nm light, the refractive index of water changes from 1.335 to 1.324. However in a metal, gold for instance, switching from 532 nm to 1064 nm changes the refractive index of gold from 0.467 to 0.285.

So it seems that the speed light travels in gold has a much larger dependency on wavelength than water does. I wanted to understand where this comes up, so I figured that calculating the speed of light for a certain medium would go back to the equation c=[εoμo]-1/2. However this time, instead of permittivity and permeability in a vacuum, we would have permittivity and permeability in gold (or whatever material you are curious about). I tried looking around the internet to find how you would calculate these new constants, but I can't figure it out.

If anybody could enlighten me that would be cool! Thanks.

2. Jul 27, 2014

### davenn

hi skate_nerd

don't think light is going to pass through gold its opaque to light

If you have any specific questions after reading that

Dave

3. Jul 27, 2014

### skate_nerd

Thanks Dave! That was really enlightening...I guess for a more thorough understanding I'll have to wait a month until I start my first Solid State Physics class.

Question: Is the end of this FAQ saying that determining the speed of light in a given material (assuming the photons are outside of the "absorption bandwith") must be derived with a case to case basis, with some sort of formula or process for doing so? Or is this something that is usually determined experimentally? Maybe both?

4. Jul 27, 2014

### davenn

I will let some one else answer that, it's outside my field of expertise

Dave

5. Jul 27, 2014

Staff Emeritus
There is no problem measuring the speed of light in opaque media. You use something called Brewster's Angle.

6. Jul 27, 2014

### phinds

Huh? I thought Brewster's angle applied to TRANSPARENT media. How does light pass through an opaque media like gold???

7. Jul 27, 2014

### davenn

Brewster's Angle ... did that for minerals in thin sections with polarisers (at uni a long time ago), but in thin section the minerals were translucent rather than opaque

But how do you go from angle measurement to speed of light measurement ?
couldn't find anything in google relating to opaque materials such as metal etc
They were all referring to transparent or translucent materials

Dave

8. Jul 27, 2014

### davenn

yeah, that had me wondering too hence my last post

Dave

9. Jul 27, 2014

### skate_nerd

This is my point exactly...I am aware of Brewster's angle, and it makes sense to me that to calculate the speed of light in anything translucent you would just need to find the speed of light in air experimentally and then from there you could employ Brewster's angle to find the index of refractive and hence the speed of light in any translucent media.

I figured initially that there has to be some empirical equation or quantum mechanical calculation you can go through to find the speed of light in any media. If the solid state physics explanation omitted in the FAQ davenn provided is too complicated or sophisticated for me to understand than I can settle for waiting for my solid state class.

10. Jul 27, 2014

### davenn

Yes any media AS LONG as its transparent or translucent

you cannot have light going through bricks, wood, iron or any other metal etc
like gold as you stated in your first post

Dave

11. Jul 27, 2014

### skate_nerd

Just for a little background:
What brought this up originally was that I have been working in a Quantum Optics lab as of late, and I am trying to reproduce part of a thesis experiment that a classmate just finished last semester. This thesis explored Plasmonic Resonant Solitons in Metallic Nanosuspensions. Previously I had done experiments using optical traps and became pretty familiar with how these work and the things you can do with them. Creating solitons in nanosuspensions with things like silica rods made sense to me, but when reading this paper and seeing the ways refractive indices differ in metallic substances I became curious, and made this post.

So I have seen in action how light can indeed be transmitted through seemingly opaque materials. The FAQ davenn provided helped me understand how that works. But like I said before, I'm still curious about the way one can calculate -- through straight mathematics -- the speed of light in these opaque media that transmit certain intervals of frequencies of light.

12. Jul 27, 2014

Staff Emeritus
Wikipedia has a nice drawing - you need to measure the incident angle at which the reflected light is 100% polarized. You do not need to measure the transmitted light. You can use this to measure the speed of light in materials that you would never think you could measure the speed of light in - like coal.

13. Jul 27, 2014

Staff Emeritus
But most materials are transparent enough - you only need it transparent for a few dozen wavelengths. Even coal works. Metals (like gold) are tricky - first, you are really looking mostly at the oxide layer (if it has one), and second, the free electrons in metals complicate matters: you can, for some wavelengths, get refractive indices below one.

14. Jul 27, 2014

### phinds

Ah ... that makes sense. Thanks.

15. Jul 28, 2014

### DrDu

The dielectric function of absorbing substances can be calculated from their reflectivity, this is how it is determined for metals like gold. For absorbing substances $\epsilon$ takes on complex values, the imaginary part being related to absorption.
In optics one usually choses the convention $\mu_r=1$, so that all optical effects are contained in the dielectric function alone (which may become a function of both frequency and wavenumber).
It is also possible to calculate the dielectric function ab initio from quantum mechanics. For the case of a gas of free electrons this is exemplified in most clases on solid state physics and is known as the Lindhard dielectric function.

16. Jul 28, 2014

### skate_nerd

Ah! Thank you! This is precisely the answer I was looking for. Much appreciated DrDu.