Finding the Index of Refraction from Pressure & Temp

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Discussion Overview

The discussion revolves around determining the index of refraction of air based on temperature and pressure conditions. Participants explore theoretical approaches, practical applications, and specific equations related to the topic.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant inquires about finding the index of refraction using temperature and pressure data, noting the ability to calculate air densities.
  • Another participant provides a resource that calculates the refractive index based on various atmospheric conditions, asking about the specific application of the inquiry.
  • A different participant suggests looking up the dielectric constant at different densities and provides a formula relating the dielectric constant to number density, clarifying the use of symbols.
  • One participant asserts that the dielectric constant for air at 1 atm is 1.00059 but questions its validity across all temperatures.
  • Another participant responds that the dielectric constant will vary with temperature and pressure, indicating that denser air results in a higher value.
  • A participant asks if there is a specific equation linking density to the index of refraction.
  • Another participant claims to have provided the relevant equation and suggests that (n-1) is proportional to air density.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the applicability of the dielectric constant across different temperatures and pressures, indicating that multiple views on the relationship between density and the index of refraction exist.

Contextual Notes

There are limitations regarding the assumptions made about the dielectric constant and its dependence on environmental conditions, which remain unresolved in the discussion.

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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