A_3MJFb0CQU/hqdefault.jpg' alt='Partial Fraction Calculator Program' title='Partial Fraction Calculator Program' />Engineering Metrology Toolbox. Index of Refraction of Air. Jack A. Stone and Jay H. Zimmerman. I.   Introduction. This web page can be used to calculate the refractive index of air for a given wavelength of light and given atmospheric conditions air temperature, pressure, and humidity. The web page also calculates the wavelength in ambient air, from the vacuum wavelength vac and the refractive index n, through the relationship 1It is the wavelength in air that determines the basic length scale of measurements performed with laser interferometers. This page is intended to serve as an aid to people doing interferometry who wish to check their own calculations of the refractive index against this NIST calculation. At present the web page calculates only the standard index of refraction the phase index certain modulated light, multi frequency, or pulsed laser applications require the group index to properly account for the effects of the atmosphere. The following text discusses some issues relevant to the calculation of index of refraction, provides guidance relating to the input parameters on the web page, and discusses the uncertainty of the results. Various points on the web page shown in blue hypertext are linked to relevant sections of this article. II.   Edln or Ciddor Guidance in Choosing the Equation. To improve this Volume of a circular truncated cone Calculator, please fill in questionnaire. Partial Fraction Calculator Program' title='Partial Fraction Calculator Program' />Two basic methods for calculating the refractive index are available here an equation developed by Ciddor. D Art Software on this page. Edln equation. 2,3,4 as modified by Birch and Downs and with an additional modification of our own. We suggest that, unless you are an expert in the field with a specific reason to choose one equation over the other, there is no need to worry about the small differences between the two equations you can choose either one and need not read any further. The Birch and Downs version of the Edln equation is probably the most commonly used equation for calculating index of refraction of air for precision measurements at temperatures near 2. C 6. 8 F. A very similar equation has been developed by Bonsch and Potulski. Ciddor. 1 and Reger. Ciddor should give somewhat better results than Birch and Downs over a broader range of wavelengths and under extreme environmental conditions of temperature, pressure, and humidity. For this reason the Ciddor equation has been adopted by the International Association of Geodesy IAG as the standard equation for calculating index of refraction the equation is believed to provide more accurate results under the more extreme temperature and humidity conditions of interest for geodetic surveying. In fact, the Edln equation includes approximations for the water vapor term that are only accurate near 2. C, and consequently the equation can be in error at high temperature and humidity. When temperatures approach 3. C and high humidity is present, the BirchDownsEdln equation will clearly not give as good results as does Ciddor. Under these circumstances the BirchDownsEdln equation may not even be superior to the much simplified version of the Edln equation given in Appendix B. When the temperature increases to 5. C with 1. 00  humidity, this error in the BirchDownsEdln water vapor term rises to 51. However, a very simple improvement of the water vapor term, as described in Section III. Comments Regarding the Calculations, eliminates most of the differences between BirchDownsEdln and the Ciddor equation at high temperature and humidity. As can be seen in Section III, after this modification of the BirchDownsEdln equation, in almost all circumstances of practical interest the differences between the two equations are small relative to the basic uncertainty of the equations. This result gives us good confidence in the two equations at the quoted level of uncertainty except under extreme conditions. Furthermore, it is difficult to imagine the realistic need for ultra precision measurements, requiring an accuracy in the refractive index better than a few parts in 1. F23c%2F23c01ca0-fd2e-4418-a940-70e5cfb723e6%2FphpKncM4x.png' alt='Partial Fraction Calculator Program' title='Partial Fraction Calculator Program' />C, or at 6. C with 1. Note that there have been no direct experimental measurements to support either equation under these environmental extremes. A6FEo4kvI/hqdefault.jpg' alt='Partial Fraction Calculator Program' title='Partial Fraction Calculator Program' />She Loves Math A free math website that explains math in a simple way, and includes lots of examples Includes Elementary Math, PreAlgebra, Algebra, PreCalculus. Nevertheless, under some circumstances the Ciddor equation might be expected to give marginally better results, because it has been developed with broader applicability in mind based very directly on BIPM density equation of reference 1. III.   Comments Regarding the Calculations. For a detailed explanation of the Edln equation, see Appendix A and references 2, 3 and 4. It is important to note that for the calculations on this web page we use a slight modification of the water vapor term given by Birch and Downs in reference 4. The water vapor term, equation 3 of reference 4, is written in a temperature independent form and hence is only valid at temperatures very near 1. C the temperature at which the constants were fitted. When dealing with temperatures much different from 1. C, the accuracy of the water vapor term can be significantly improved if it is multiplied by the ratio 2. Celsius temperature, so as to account for the change in density with changing temperature in the ideal gas approximation. The modified version of the water vapor correction BirchDowns equation 3, is then 2where ntpf ntp is the water vapor correction, f is the partial pressure of water vapor, and is the wave number. This equation is written using the notation and symbols of Birch and Downs. We use a different notation in the rest of this article. Rewritten in our notation, equation 2 appears in Appendix A as equation A4. This modification of the Birch and Downs formula eliminates most of the discrepancy between the Birch and Downs formulation and the calculations of Ciddor at high temperature and humidity. For a detailed explanation of the Ciddor Equation, see reference 1 and Appendix A. Our calculation differs from Ciddor only in two minor aspects. First, we use a slightly different method to calculate saturation vapor pressure to relate dew point temperature to mole fraction. Second, we use the 1. CODATA value for the molar gas constant see equation A3. The resulting disagreements in the refractive index are only a few parts in 1. See the discussion of Humidity in Section IV and see Section V, Calculating Saturation Vapor Pressure. IV.   Comments Regarding Inputs to the Equations. Vacuum Wavelength. The web page will accept input values for vacuum wavelength ranging from 3. Ciddor. Birch and Downs claim a range of validity only from 3. Note that the visible region extends from approximately 4. The standard red helium neon laser, used for many metrology applications, has a wavelength in vacuum that is within a few parts in 1. Infrared diode lasers commonly operate at wavelengths ranging from the visible up to 1. Pressure. Atmospheric pressure may be expressed in a variety of common pressure units. Soul Reaver Torrent Pc Italia. In SI units, the web page accepts inputs ranging from 1. Pa to 1. 40 k. Pa, but a warning is issued if the pressure falls outside of the more realistic range from 6. Pa to 1. 20 k. Pa. There is no reason to doubt the validity of the equations at least over the range 6. Pa to 1. 20 k. Pa, although Ciddors suggested lower pressure limit 8. Pa is slightly higher than suggested here and is perhaps unnecessarily restrictive for work at high elevation. Usmt There Is A Problem With This Installer Package Windows'>Usmt There Is A Problem With This Installer Package Windows. Standard atmospheric pressure at sea level is conventionally taken to be 1. Pa approximately 7.