# Speed of light in unusual materials

by skate_nerd
Tags: light, materials, speed, unusual
 P: 57 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.
PF Gold
P: 2,756
 So it seems that the speed light travels in gold
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
P: 57
 Quote by davenn http://www.physicsforums.com/showthread.php?t=511177 If you have any specific questions after reading that then ask them Dave
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?

PF Gold
P: 2,756
Speed of light in unusual materials

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

Dave
 Emeritus Sci Advisor PF Gold P: 16,472 There is no problem measuring the speed of light in opaque media. You use something called Brewster's Angle.
PF Gold
P: 6,514
 Quote by Vanadium 50 There is no problem measuring the speed of light in opaque media. You use something called Brewster's Angle.
Huh? I thought Brewster's angle applied to TRANSPARENT media. How does light pass through an opaque media like gold???
 Sci Advisor PF Gold P: 2,756 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
PF Gold
P: 2,756
 Quote by phinds Huh? I thought Brewster's angle applied to TRANSPARENT media. How does light pass through an opaque media like gold???
yeah, that had me wondering too hence my last post

Dave
P: 57
 Quote by davenn 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
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.
PF Gold
P: 2,756
 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
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
 P: 57 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.
 Emeritus Sci Advisor PF Gold P: 16,472 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.
Emeritus