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CONVERSION OF WAVELENGTHS IN AIR TO WAVE NUMBERS IN VACUUM AND VICE VERSA
APPENDIX I CONVERSION OF WAVELENGTHS IN AIR TO WAVE NUMBERS IN VACUUM AND VICE VERSA The equation t>vac = l/w\ a i r permits the conversion of a wavelength in standard air to a wave number in vacuum, provided the value of w, the refractive index for standard air, is known. (Standard air is dry air containing 0.03% by volume of C0 2 at normal pressure 760 mm Hg and having an air temperature of 15°C. ) Edlén's1 dispersion formula for standard air is given by - 1 4. w> ft x m-8 -u 2 949 810 , "stdair - 1 + 6432.8X 10 4- 1 4 6 x 10 e . v2 + 4 1
25 540 _ v*
x 10 e
n
Δν
ff-A)
where v is the wave number expressed in cm"1. Based on the work of Edlén, extensive tables of wave numbers were prepared by Coleman, Bozman, and Meggers2 for the waveo
length from 2000 A-1000 μ. Prior to this publication, the work of Penndorf3 dealt with the values for the refractive indexes of standard air for the spectral region between 0.2 and 20 μ. o
Recently, Edlén prepared conversion tables for λ > 10, 000 A suitable for use with desk calculators. They are reproduced as Tables 1.1 and 1.2 of this Appendix, and a few examples are given to illustrate their use. Table 1.1: This table can be used for the conversion of air wavelengths to vacuum wave numbers (expressed in cm"1). For example (Table I, Chapter I) in order to convert X air = 12802.737 A (12802.737 x 10"8 cm) to VV2LC (cm"1), we note that 12802.737 (X alr ) occurs between the numbers 12740 and 12807 in Table 1.1. The vertical line between these two numbers terminates in the digit 3. At the left, in column 1, we find the reciprocal index of standard air (n_1) to be 0.9997265. To this value we link the digit 3 so that it becomes 0.99972653; therefore 0-99972653 'vac- 12802.737 x 10"8
g 7808.694
cm-t
Table 1.2: This table is to be used to obtain Xa 7287.393 cm - 1 , this value can be located between the numbers 7293 and 7249 in Table 1.2. X
B. Edlén, J. Opt. Soc. Am. 43, 339 (1953). C . D. Coleman, W. R. Bozman, and W. F. Meggers, Natl. Bur. Std. (U.S.), Monograph 3, Vols. I and Π (1960). 3 R. Penndorf, J. Opt. Soc. Am. 47, 176 (1957). 2
177
The vertical line between these two numbers terminates in 6 and the horizontal line connecting them leads to 0.9997266 for w"1. Proceeding as above, . . _ 0.99972666 _ Aair - 7287.393 X 10~8 "
_ · 1i r3 7n 1R8 5 7777 A '
In other words, the numbers given in both tables help us only to locate the last digit o
for w"1. No interpolations are necessary. In Table 1.1 the numbers following X20108 A are given in microns. It should be recalled that it is important to determine the wavelength correction required for nonstandard air conditions. The following formula from Edlén can be used: Γ ΊΓ0.0013882/> 1 ^
X20 - λ 2
=
[Δλ2 - AMVXi)JLfTÖ^Ö367* " il
%
<*"Β>
where X2° = unknown wavelength at standard temperature and pressure X 2 = unknown wavelength as measured in nonstandard air X ! = reference wavelength (for instance, if the green radiation from Hg198 is used, o
X1 = 5460.7529 A in standard air) and
* = vacuum corrections for X 2 and X x (for instance, the vacuum correction for Hg198 green line is 1.5175 A) p = atmospheric pressure in millimeters of Hg t
= temperature in °C
In high precision work, an additional correction should be made for the water vapor. This is given by X° - X2 = [+0.63 (1 + λ , Α ι ) (*» - "i)/]
x
M"9
C-C) -1
where X2° - X2 and X x are expressed in angstroms and v2 and vx in cm ; / is in millimeters of Hg of water vapor. For instance, if X 2 = 4046 A, X x = 5460 A, and/ = 10 mm of Hg, the o
correction due to water vapor is +0.00007 A.
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length from 2000 A-1000 μ. Prior to this publication, the work of Penndorf3 dealt with the values for the refractive indexes of standard air for the spectral region between 0.2 and 20 μ. o
Recently, Edlén prepared conversion tables for λ > 10, 000 A suitable for use with desk calculators. They are reproduced as Tables 1.1 and 1.2 of this Appendix, and a few examples are given to illustrate their use. Table 1.1: This table can be used for the conversion of air wavelengths to vacuum wave numbers (expressed in cm"1). For example (Table I, Chapter I) in order to convert X air = 12802.737 A (12802.737 x 10"8 cm) to VV2LC (cm"1), we note that 12802.737 (X alr ) occurs between the numbers 12740 and 12807 in Table 1.1. The vertical line between these two numbers terminates in the digit 3. At the left, in column 1, we find the reciprocal index of standard air (n_1) to be 0.9997265. To this value we link the digit 3 so that it becomes 0.99972653; therefore 0-99972653 'vac- 12802.737 x 10"8
g 7808.694
cm-t
Table 1.2: This table is to be used to obtain Xa 7287.393 cm - 1 , this value can be located between the numbers 7293 and 7249 in Table 1.2. X
B. Edlén, J. Opt. Soc. Am. 43, 339 (1953). C . D. Coleman, W. R. Bozman, and W. F. Meggers, Natl. Bur. Std. (U.S.), Monograph 3, Vols. I and Π (1960). 3 R. Penndorf, J. Opt. Soc. Am. 47, 176 (1957). 2
177
The vertical line between these two numbers terminates in 6 and the horizontal line connecting them leads to 0.9997266 for w"1. Proceeding as above, . . _ 0.99972666 _ Aair - 7287.393 X 10~8 "
_ · 1i r3 7n 1R8 5 7777 A '
In other words, the numbers given in both tables help us only to locate the last digit o
for w"1. No interpolations are necessary. In Table 1.1 the numbers following X20108 A are given in microns. It should be recalled that it is important to determine the wavelength correction required for nonstandard air conditions. The following formula from Edlén can be used: Γ ΊΓ0.0013882/> 1 ^
X20 - λ 2
=
[Δλ2 - AMVXi)JLfTÖ^Ö367* " il
%
<*"Β>
where X2° = unknown wavelength at standard temperature and pressure X 2 = unknown wavelength as measured in nonstandard air X ! = reference wavelength (for instance, if the green radiation from Hg198 is used, o
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* = vacuum corrections for X 2 and X x (for instance, the vacuum correction for Hg198 green line is 1.5175 A) p = atmospheric pressure in millimeters of Hg t
= temperature in °C
In high precision work, an additional correction should be made for the water vapor. This is given by X° - X2 = [+0.63 (1 + λ , Α ι ) (*» - "i)/]
x
M"9
C-C) -1
where X2° - X2 and X x are expressed in angstroms and v2 and vx in cm ; / is in millimeters of Hg of water vapor. For instance, if X 2 = 4046 A, X x = 5460 A, and/ = 10 mm of Hg, the o
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