Re: [Phys-l] Refractive index of gases

[John Denker <jsd@av8n.com>]

I wrote:

> > Or look in Feynman.


On 02/08/2007 08:29 PM, alex brown wrote:
> Thanks John,
>
> However, it still leaves me with having to look up constants....  But more worryingly can I say
> that the permitivity of the gas as a whole is the sum of the permitivyt of the atoms that it is
> made up of?  I don't know  ?

1) Indeed there is a linear relationship, in the low-density limit.

2) I don't want to nitpick the terminology, but properly speaking
 the permittivity is not what you want to be summing, but rather
 the refractivity:
   http://scienceworld.wolfram.com/physics/Refractivity.html


>> Or look in Feynman.

Maybe I need to be more explicit.

Volume I chapter 31 is entitled "The Origin of the Refractive Index".
Equation 31.19 gives a nice simple expression, valid in the low-density
limit.

Volume II chapter 32 revisits this topic in more detail, in particular
considering dense materials also, including the Clausius-Mossotti
formula, equation 32.32.  The bottom of page 32-6 explains in detail
how to reconcile the low-density limit with the general result.

Section 32-5 is "The index of a mixture".  See in particular equation
32.37.  For low-density materials (such as gasses), write the index as
(1+refractivity) and expand n^2 to first order.

=====================

> can I say
> that the permitivity of the gas as a whole is the sum of ....

As a famous man once said, "To first order, everything is linear".
That's actually not /strictly/ true, but it's true enough to tell
you what to expect in this case.

The Clausius-Mossotti formula is definitely nonlinear, but you can
easily show that it becomes linear in the low-refractivity limit.

=====================

Sometimes hints are just hints ... but sometimes hints are a backhanded
way of super-hyper-ultra-emphasizing something.

If something is discussed in Feynman, it's probably going to be well worth
reading.  Therefore if somebody even vaguely hints that a topic might be
discussed there, you should more-or-less drop everything and go check.