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Effect of Relative Humidity on Index of Refraction
From: Fred Hebard
Date: 2003 May 3, 12:24 -0400
From: Fred Hebard
Date: 2003 May 3, 12:24 -0400
I like this guy Snell, whose law says that we don't have to worry about the refractive index above our elevation! I evaluated the formula in the Smithsonian Meteorological Tables on page 389, to examine the effect of relative humidity on the index of refraction. By my calculation, it doesn't show up until the fifth place in the index of refraction. So, for the purposes of nautical astronomy, it needn't be considered. (And one would expect this since the Nautical Almanac doesn't consider it)! Here are the results in tabular form. p is the atmospheric pressure in millimeters of mercury. Sat vp is the saturation vapor pressure of water in _inches_ of mercury. t is the temperature in degrees Celcius. lamda is the wavelength of light in micrometers. rh is the percent relative humidity. f is the vapor pressure of water at that humidity. term1 is the first term of the Smithsonian formula, which accounts for atmospheric pressure. term2 is the second term, which accounts for water vapor pressure. n is the index of refraction. I may not have converted properly between inches of mercury for water at saturation vapor pressure for that temperature (Sat vp) and the partial pressure from water in millimeter (f), but, if my evaluation of the formula is correct, an improper conversion would not be significant. You can see that term1, the effect of atmospheric pressure, dominates the numbers, and that the index of refraction is not strongly affected by humidity. p Sat vp t lamda rh f term1 term2 n 760 0.04477 0 0.5461 0 0 297.7584 0 1.0002977584 760 0.04477 0 0.5461 100 0.113716 297.7584 0.006621 1.0002977518 760 0.05646 5 0.5461 0 0 292.3885 0 1.0002923885 760 0.05646 5 0.5461 100 0.143408 292.3885 0.0082 1.0002923803 760 0.0708 10 0.5461 0 0 287.2082 0 1.0002872082 760 0.0708 10 0.5461 100 0.179832 287.2082 0.010101 1.0002871981 760 0.08832 15 0.5461 0 0 282.2077 0 1.0002822077 760 0.08832 15 0.5461 100 0.224333 282.2077 0.012382 1.0002821953 760 0.1096 20 0.5461 0 0 277.3778 0 1.0002773778 760 0.1096 20 0.5461 100 0.278384 277.3778 0.015103 1.0002773627 760 0.13534 25 0.5461 0 0 272.7099 0 1.0002727099 760 0.13534 25 0.5461 100 0.343764 272.7099 0.018337 1.0002726915 760 0.16631 30 0.5461 0 0 268.1959 0 1.0002681959 760 0.16631 30 0.5461 100 0.422427 268.1959 0.022162 1.0002681738 760 0.20342 35 0.5461 0 0 263.8285 0 1.0002638285 760 0.20342 35 0.5461 100 0.516687 263.8285 0.026667 1.0002638018 760 0.24767 40 0.5461 0 0 259.6005 0 1.0002596005 760 0.24767 40 0.5461 100 0.629082 259.6005 0.031949 1.0002595685