How Does Temperature Gradient Affect Refractive Index in Fluid Thermodynamics?

[Relena]

Does anyone have an idea about a formula relating the refractive index of a medium
to the temperature gradient (Generally)?

 

[Andy Resnick]

There's a few formulas out there- the temperature affects the density, which affects the refractive index:

http://pirika.com/chem/TCPEE/RI/ourRI.htm

http://www.iop.org/EJ/abstract/0022-3727/20/4/019

http://www.blackwell-synergy.com/doi/abs/10.1111/j.1151-2916.1955.tb14581.x?cookieSet=1&journalCode=jace

 

[Relena]

That was enlightening ..

but after reading the Lorentz-Lorenz equation I became more confused due to the factor called "molar refractivity"
and it's equal to the volume occupied by one mole of a substance.
A=RT(n^{2}-1)/3P
Isn't the volume varying due to temperature? ,then the molar refractivity changes with temperature, and the refractive index would be affected only if we considered the ratio between temperature and pressure to remain constant??

I don't know if this is right (because mirage occurs) .
but how can a slight temperature gradient (about 5^{o}C/m) to cause this deviation in the path of light??

 

[Andy Resnick]

Ah- you are interested in mirages; why didn't you just ask about that?

http://www.atoptics.co.uk/atoptics/sunmir2.htm

http://en.wikipedia.org/wiki/Mirage

http://www.crystalinks.com/mirage.html

Don't forget that for mirages the optical path length is very long- many hundreds of meters. Small differences accrue over that distance.

Edit: fixed typo.

 

[Relena]

Well...
I know it takes a long distance for light to be totally reflected..

But in asphalt mirage you can see the reflection of a car on the road .
It doesn't take so long for light ... however it depends more on the sharpness of the gradient refractive index ( and subsequently the temperature gradient).. however the refractive index of air doesn't vary so much .. but it depends also on the distance in which the refractive index changed.

This simply makes a question: What is the minimum distance between you and the image that undergoes mirage.. to observe it's reflection clearly?
(of course DEPENDENT on temperature)

 

[Relena]

OK it seems that my question isn't clear??
one of the uses of gradient refractive index is making lenses (see the article)

so am I wrong if I thought we can make such a lens from a fluid (ex: air)
such that the gradient refractive index is nearly the same?

http://en.wikipedia.org/wiki/Gradient-index_optics

 

[Claude Bile]

In principle, yes it is possible to make a GRIN lens by heating a fluid.

Is it feasible in practice though? Well that depends on the magnitude of refractive index change you can get at a reasonable temperature (i.e. the dn/dT of the fluid). You would also need to manage the convection that inevitably arises when inducing a thermal gradient in a fluid.

In response to your previous post (post #5), the limitation on viewing mirages is not distance per se, it is viewing angle (which could be phrased as a distance limit for some given viewing height).

Claude.

 

[Relena]

thanx that's what I wanted to know .

I'm now trying to find a mathematical model relating the refractive index to the temperature gradient.
thus study the effect of fluid thermodynamics on light