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2.5.7 Refractive index of gases

Refractive index of air

The wavelength λair of a radiation in air is related to its vacuum value λvac by λvac = nλair, where n is the refractive index. For standard air (dry air at 15 °C and 101 325 Pa, containing 0.045% by volume of carbon dioxide) the refractive index ns is given by the dispersion equation (Birch, Metrologia, 1994, 31, 315)

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(ns − 1) × 108 = 8 342.54 + 2 406 147(130 − σ2)−1 + 15 998(38.9 − σ2)−1


where σ = 1/λvac and λvac is expressed in μm. This equation is based upon observations within the range 200 nm to 2 μm, and is in better agreement with recent measurements than the previous equation (Edlén, Metrologia, 1966, 2, 71) mainly due to the increase in ambient carbon dioxide levels.
   In the visible region (405–705 nm) the following approximate expression is more convenient and gives a maximum discrepancy of only 1.4 × 10−8,

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ns − 1 = 0.047 2326(173.3 − σ2)−1


    For air at a temperature t °C and a pressure p Pa, the refractivity is given by the equation

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ntp − 1 = (ns − 1) × 

 p[1 + p(60.1 − 0.972t) × 10−10]

96 095.43(1 + 0.003 661t)

The refractivity of water vapour is less than that of air, so that if the air is moist its refractive index will be smaller than the value calculated for dry air. This water vapour term is dependent upon wavelength. In the visible region (405–644 nm) the relationship is

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ntp fntp = −f (3.7345 − 0.0401σ2) × 10−10,


where ntp f is the refractive index of air containing water vapour at a partial pressure of f Pa, the total pressure still being p. This equation is valid only for conditions not deviating very much from normal laboratory conditions (t = 20 °C, p = 100 000 Pa, f = 1500 Pa).



Refractive indices of gases

Refractive index for the wavelength 589.3 nm (mean of sodium D lines) at a pressure of 101 325 Pa and temperature of 0 °C, relative to a vacuum.

Laser radiation

Gas

Refractive index

Gas

Refractive index

 

 

 

 

Acetone    .    .    .    .    .    .

1.001 090

  Hydrochloric acid  .    .    .    .

1.000 447

Air       .    .    .    .    .    .    .

1.000 292

  Hydrogen    .    .    .    .    .    .

1.000 132

Ammonia       .    .    .    .    .

1.000 376

  Hydrogen sulphide .    .    .    .

1.000 634

Argon  .    .    .    .    .    .    .

1.000 281

  Methane      .    .    .    .    .    .

1.000 444

Benzene    .    .    .    .    .    .

1.001 762

  Methyl alcohol  .    .    .    .    .

1.000 586

Bromine    .    .    .    .    .    .

1.001 132

  Methyl ether     .    .    .    .    .

1.000 891

Carbon dioxide   .    .    .    .

1.000 449

  Nitric oxide  .    .    .    .    .    .

1.000 297

Carbon disulphide    .    .    .

1.001 481

  Nitrogen       .    .    .    .    .    .

1.000 298

Carbon monoxide    .    .    .

  1.000 338

  Nitrous oxide    .    .    .    .    .

1.000 516

Chlorine    .    .    .    .    .    .

1.000 773

  Oxygen      .    .    .    .    .    .

1.000 271

Chloroform    .    .    .    .    .

1.001 450

  Pentane      .    .    .    .    .    .

1.001 711

Ethyl alcohol  .    .    .    .    .

1.000 878

  Sulphur dioxide    .    .    .    .

1.000 686

Ethyl ether     .    .    .    .    .

1.001 533

  Water vapour      .    .    .    .

1.000 256

Helium     .    .    .    .    .    .

1.000 035

 

 

 

 

 

 

     Value for white light .


Refractive indices of gases at radio frequencies

Values below are for dry gases at 0 °C, 101.325 kN m−2. The quoted uncertainty limits are about 3σ (σ = standard error of the mean).

Gas

(n − 1)/10 −6

 

 

Air (CO2 free)     .    .    .    .    .    .

288.15 ± 0.1  

Deuterium      .    .    .    .    .    .    .

134.8 ± 0.3  

Helium       .    .    .    .    .    .    .    .

35.0 ± 0.2  

Carbon dioxide   .    .    .    .    .    .

494   ± 1.0  

Hydrogen      .    .    .    .    .    .    .

136.0 ± 0.2  

Nitrogen        .    .    .    .    .    .    .

294.1 ± 0.1  

Oxygen    .    .    .    .    .    .    .    .

266.4 ± 0.2  

Water vapour†    .    .    .    .    .    .

60.7 ± 0.1  

 

 

                  At 20 °C, 1.333 kPa (10 mmHg).


Refractive index of moist air at radio frequencies

The following formula has been derived from measured values and the gas laws, and holds over a wide range of conditions:

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(n −1) × 106

0.77624

 p1 +

1.3306

 p2 +

0.6470  

1 +

5748

 p3

T

T

T

T


Where p1 = partial pressure of dry air in Pa
          p2 = partial pressure of carbon dioxide in Pa
          p3 = partial pressure of water vapour in Pa
           T = thermodynamic temperature in K.


K.P.Birch

 

 

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