Finding the Index of Refraction from Pressure & Temp

In summary, the conversation discusses the relationship between Snell’s law and the index of refraction for air. The conversation also touches upon finding the index of refraction using temperature, pressure, humidity, and CO2 content. The dielectric constant for air is also mentioned, with the understanding that it varies with temperature and pressure. The discussion also includes an equation that relates the density to the index of refraction.
  • #1
Az83
7
0
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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  • #2
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?
 
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  • #3
well. I think you could look up the dielectric constant ([itex]\epsilon[/itex], where [itex]n^2=\epsilon[/itex]) at different densities. but also, if you know the dielectric constant at some given number density ([itex]n_1[/itex]) then to find it at a different density you could use
[tex]
\frac{\epsilon(n_2)-\epsilon(n_2)}{\epsilon(n_1)-1}=\frac{n_2-n_1}{n_1}
[/tex]

...and, sorry for using the symbol n for two different things... my bad, in the equation it is number density, not index of refraction
 
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  • #4
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?
 
  • #5
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.
 
  • #6
Is there an equation that relates the density to the index of refraction?
 
  • #7
i gave it to you
 
  • #8
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.
 

Related to Finding the Index of Refraction from Pressure & Temp

1. What is the index of refraction?

The index of refraction is a measure of how much a material slows down the speed of light passing through it. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material.

2. How is the index of refraction affected by pressure and temperature?

The index of refraction is directly proportional to both pressure and temperature. As pressure increases, the density of the material increases, causing the speed of light to decrease and the index of refraction to increase. Similarly, as temperature increases, the molecules in the material vibrate more, leading to a decrease in the speed of light and an increase in the index of refraction.

3. What is the formula for finding the index of refraction from pressure and temperature?

The formula for finding the index of refraction from pressure and temperature is n = c/v, where n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the material. This can also be written as n = n0 x (T0/T) x (P/P0), where n0, T0, and P0 represent the values of the index of refraction, temperature, and pressure at a standard reference state.

4. How is the index of refraction used in scientific research?

The index of refraction is an important parameter in various fields of science, including optics, materials science, and atmospheric science. It is used to calculate the critical angle for total internal reflection, to determine the composition and properties of materials, and to study the behavior of light in different mediums.

5. Can the index of refraction be measured directly?

Yes, the index of refraction can be measured directly using a refractometer or by measuring the angle of refraction when light passes through a material. However, in some cases, it may be more practical to calculate the index of refraction using the formula mentioned above.

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