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2.5.7 Refractive index of gases

Refractive index of air

The wavelength λ_air of a radiation in air is related to its vacuum value λ_vac by λ_vac = nλ_air, 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 n_s is given by the dispersion equation (Birch, Metrologia, 1994, 31, 315)

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

where σ = 1/λ_vac and λ_vac 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,

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

	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

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

where n_{tp 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

    ^† 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).

                 ^† 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:

	(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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