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    Re: Dip and the refractive invariant
    From: Paul Hirose
    Date: 2013 Apr 22, 12:16 -0700

    Bruce J. Pennino wrote:
    > Paul,  I have one set of dip data that indicates a value of dip 
    significantly higher than would be predicted in the NA or that I've measured 
    elsewhere.  Interestingly, it is  a rushed data set at one of my lowest HoE.  
     The wind was blowing smog in my face from Long Island and NYC. I was 
    sighting over Long Island Sound. Considering Frank's pictures and your 
    analysis, how does smog influence refraction.  I would imagine I was in the 
    same smog as the horizon.... your thoughts?
    If it was not a false horizon, a dip greater than expected suggests the
    indices of refraction at the observer and sea level were abnormally
    similar. In fact, if they are identical, refracted dip equals the
    geometric dip.
    I don't know how smog would affect refraction.
    I wrote:
    > Combining all the above, dip (radians) = √(2 * (dn + h))
    > where dn is the difference in the refractive indices of the air at the
    > sea surface and at the observer (negative if the latter is less), and h
    > is the height of eye in earth radii.
    For a more convenient formula, change h (height of eye) to meters
    instead of Earth radii. The value of dn must be multiplied by the same
    factor to keep the sum (dn + h) valid. Let dn′ = dn * 6371000, and h
    = height of eye in meters. Then:
    dip (radians) = √(2 * (dn′ / 6371000 + h / 6371000))
    = √(dn′ / 3185500 + h / 3185500)
    = √(1 / 3185500) * √(dn′ + h)
    dip (arcmin) = 180 / π * 60 * √(1 / 3185500) * √(dn′ + h)
    dip (arcmin) = 1.926 * √(dn′ + h)
    where dn′ = 6371000 * ((refractive index at eye) - (refractive index at
    h = height of eye (meters)
    Test the formula with my previous example at 10 meters height of eye.
    The value of dn was -2.65e-7, so dn′ = -1.69. Dip = 1.926 * √(-1.69 +
    10) = 5.55′, which agrees with the almanac and the computation in my
    previous message.
    In other words, the decrease in refractive index of the air between
    sea level and the eye is equivalent to a reduction in height of eye by
    that many Earth radii.
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