Finding the Index of Refraction from Pressure & Temp

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SUMMARY

The discussion focuses on calculating the index of refraction of air based on temperature and pressure using Snell's law. The dielectric constant of air at 1 atm is approximately 1.00059, but this value varies with temperature and pressure. The relationship between air density and the index of refraction is established, indicating that (n-1) is proportional to air density. For accurate calculations, users are directed to a specific online tool that computes the refractive index based on various atmospheric conditions.

PREREQUISITES
  • Understanding of Snell's law and its application in optics.
  • Familiarity with the concept of dielectric constant and its relation to refractive index.
  • Knowledge of how temperature and pressure affect air density.
  • Basic skills in using online calculators for atmospheric properties.
NEXT STEPS
  • Research the relationship between dielectric constant and refractive index in gases.
  • Explore the effects of humidity and CO2 content on the refractive index of air.
  • Learn about advanced atmospheric modeling techniques for ray tracing calculations.
  • Investigate empirical formulas for calculating the refractive index based on varying atmospheric conditions.
USEFUL FOR

Students, physicists, and engineers involved in optics, atmospheric science, or any field requiring precise calculations of the refractive index of air under varying conditions.

Az83
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For Snell's law n2sin(theta2)=n1sin(theta1), I know that air has an index of refraction of approximately 1. But how do I find the actual value for the index of refraction if I know the temperature jump and pressure? I know that from what I am given, I can find the densities of the air, but then how do I use the densities to find the index of refraction?
 
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A Google search on
air "refractive index"
led me here:
http://www.strw.leidenuniv.nl/~mathar/progs/prWaterWeb.html
Calculates (n-1) depending on temperature, pressure, humidity, and even CO2 content of the atmosphere!

Do you happen to have a particular application or use in mind? Eg., ray tracing calculation, atmospheric distortion, solving a homework problem, other?
 
Last edited by a moderator:
well. I think you could look up the dielectric constant (\epsilon, where n^2=\epsilon) at different densities. but also, if you know the dielectric constant at some given number density (n_1) then to find it at a different density you could use
<br /> \frac{\epsilon(n_2)-\epsilon(n_2)}{\epsilon(n_1)-1}=\frac{n_2-n_1}{n_1}<br />

...and, sorry for using the symbol n for two different things... my bad, in the equation it is number density, not index of refraction
 
Last edited:
this question is for a homework problem. It seems that every source I look at, the dielectric constant for air at 1 atm is 1.00059. Is this value safe to assume for all temperatures?
 
Az83 said:
this question is for a homework problem. It seems that every source I look at, the dielectric constant for air at 1 atm is 1.00059. Is this value safe to assume for all temperatures?

No, it will change with temperature and pressure. The denser the air, the higher the value.
 
Is there an equation that relates the density to the index of refraction?
 
i gave it to you
 
Az83 said:
Is there an equation that relates the density to the index of refraction?

You can do pretty well by assuming (n-1) is proportional to the air density.
 

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