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All right, by popular request, let's keep this discussion open to the list,
then.

What we are discussing is a Fred Hebard's original question-

>Are there
>ever events in the atmosphere where astronomical or distant earthly
>objects will appear lower than they really are, rather than higher, ie.
>events where the effective index of refraction is of opposite sign to
>that usually encountered?  By effective index of refraction, I am
>trying to indicate the total refraction between the object and the
>observer rather than a local refraction.

I won't repost the details of the ensuing arguments here, so if you wish to
follow the discussion so far you will have to consult the archives.

John Brenneise said-

>OK, Treat each individual molecule of Oxygen, Nitrogen, etc as one of a
>series of plane surfaces of arbitrary orientation with which a light ray
>interacts.  In order to bend away from the mean normal would still require a
>cumulative decrease in the index of refraction along the entire arbitrary
>path from the initial entry point of the light ray into Earth's atmosphere
>to the observer's eye.
>
>If you really want to be rigorous about it, throw out Snell's Law and use
>Quantum Mechanics to model the absorption and retransmission of light from
>one molecule to another.
>
>I heartily agree that using sights lower than 15 degrees or so is
>problematic, in that a lot of variation in the density of the atmosphere is
>inevitable and the simplified quantitative models fall apart.  However, the
>question had to do with the qualitative question of whether or not light
>ever bends upwards overall.
>
>Perhaps,  if you were in space flight, you might observe an image of a star
>that was partially REFLECTED off of Earth's atmosphere.  That would be a
>case where the bend would be upwards.  But if you were in space flight,
>you'd have a wide selection of stars to choose from, and you could simply
>avoid near eclipses like this.  Perhaps someone with knowledge/experience
>with space craft guidance systems could shed some light on this, if indeed
>such systems use celestial objects as references.

My reply-

All this business about individual molecules and quantum mechanics is no
more than a distraction from the question in hand, which is one of
classical optics. It's a simple matter of schoolbook Snell's law; any
complication being due to the fact that in the atmosphere the refractive
index of the medium is continuously and smoothly varying, whereas at school
we usually applied Snell's law to discrete surfaces each of constant
refractive index.

John Brenneise has explained Snell's law in an earlier mailing.

We agree, don't we, that light entering the atmosphere, of increasing
density, will be bent toward the normal. But normal to what, I ask? Normal
to the plane of the surfaces of constant air density. Is that the same as
normal to the Earth's surface? Not necessarily. Usually, it will be, but if
there are wedge-shaped divisions between air masses of differing air
density, such as exist in a "front", then those surfaces of constant
density may have a significant slope.

I have hypothesised in a previous mailing that a star was being seen by an
observer, in such a way that the light path travelled down the sloping
interface between warm air and cold, in a front. In that case, along its
whole path the ray could be subject to a curvature which would depend on
the temperature gradient, and may add up to a significant change from the
usual predicted refraction. That, in itself, is an interesting conclusion
(if it's true). Perhaps it's on such occasions that we sometimes see such a
distorted disc, of a low Sun. Perhaps sextant observations are subject to
unpredictable error when they are made at such a front-line. Have any
studies been made of such meteorological effects on refraction? I don't
know.

True, as I have accepted, because a front is warm air overlying cold, that
curvature will normally be in such a direction as to increase the
refraction above its predicted value, not reduce or reverse it. So, to
tackle Fred's question, we have to ask if the converse situation, of a
wedge of colder air overlying warm, could ever exist. Trevor Kenchington
has suggested that was impossible, because of thermal instability. But I
have given an example where it certainly does happen, on a small scale at
least, when a layer of warm air is heated by a road surface below it. Bob
Gainer has suggested another; temperature inversion in the San Fernando
Valley, California.

That was why I suggested that the question was really one for a
meteorologist, though that's no reason to stop us speculating about it! My
own opinion is that it's highly unlikely that a situation could develop to
bend light from the sky in the opposite direction from normal, but I am
always hesitant about using the word "impossible".

George.

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