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    Re: Table A4 + elevation?
    From: George Huxtable
    Date: 2003 May 3, 10:38 +0100

    Trevor Kenchington said-
    >Is Table A4 correcting primarily for refraction in the layers of air
    >immediately above the observer or primarily for refraction higher up? If
    >the former, then I fully understand George's point: The lower pressure
    >at altitude means less refraction and Table A4 doesn't extend far enough
    >to cope with observations taken from far up a mountain but the equations
    >from which the Table was drawn should be applied to the air pressure
    >observed at Doug's location.
    >However, if the bulk of the refraction occurs much higher in the
    >atmosphere, air pressure at the observer's location can only give an
    >approximate indication of the density of the air far above but that
    >approximation would need to be based on observed surface pressure
    >standardized to sea level. Indeed, if we are dealing with substantial
    >refraction high in the atmosphere (even if there is more per metre in
    >the few metres nearest the Earth), it might be necessary to use a
    >correction drawn from Table A4 using surface pressure standardized to
    >sea level and then a second correction based on the pressure difference
    >between the observer's altitude and sea level to allow for the lack of
    >low-level refraction resulting from the observer's elevation. The
    >combination of the two corrections would presumably be intermediate
    >between what Table A4 gives for the sea-level pressure and what it would
    >give if the pressure at altitude were treated as a sea-level observation.
    I don't think Trevor has anything to worry about here.
    For all angles of altitude except very low ones, it's a VERY good
    approximation to treat refraction of light in the atmosphere as though the
    earth's surface were flat, as are any boundaries or contours of pressure or
    temperature in the air above it. It's only for light that comes in from a
    direction that's nearly tangential to the surface, that the Earth's
    curvature has to be taken into account, and that's where it all gets rather
    In the plane-parallel case, however, Snell's law applies, and then the
    overall bending of light, from its original direction, as it reaches the
    observer, is determined ONLY by the angle of incidence and the difference
    between the refractive index as it comes into the atmosphere (which is
    exactly 1, for free space) and the local refractive index at the level of
    the observer. It doesn't matter a damn what happens in-between, or where it
    happens. The index in-between may vary up or down, different layers can be
    thick or thin, but nevertheless the total overall bending will be exactly
    the same. Surprising but true (well, it surprised me, at first).
    This, I hope, will also answer some of Fred Hebard's worries. Except when
    observing bodies at low altitude, humidity or any other effect along the
    light path has no effect on the refraction: all that matters is what it's
    like at the receiving end.
    If Trevor, or Fred, or anyone else, remains unconvinced, we can argue it
    further, or I can look up some references.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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