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Subject: Effect of Relative Humidity on Index of Refraction
From: Fred Hebard (Fred@XXX.XXX)
Date: Sat May 03 2003 - 12:24:21 EDT
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
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