NavList:

   

Reply

Fred Hebard has an inquiring mind, and a tendency to ask interesting
questions. The one copied below came to me off-list

>George,
>
>A private question, which you could make public if you wish.  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.
>
>Thanks,
>
>Fred

Atmospherics is not my specialty, though I'm as willing to pontificate
about it as the next man. I'm posting Fred's question to the list, in the
hope than someone will pick it up who knows more than I do.

The quick answer is: I don't know, but think it's very unlikely.

The direction in which light is bent depends on the density-gradient of the
air through which it passes. Normally the density will decrease as the
height increases, because it's proportional to pressure, and the pressure
decreases as the height increases because there's less overburden from the
decreasing mass of air above it. So if pressure was only factor involved,
the density would always fall as the height increased, and any incoming
light ray would curve downwards slightly, to be a bit nearer the vertical.

But density (of air or any other gas) also depends on temperature. At a
constant pressure, it's inversely proportional to the absolute temperature
(Charles' Law, I think). The absolute temperature is measured on a acale in
which absolute zero is at 0 degrees, not -273deg C, so that an ambient
temp. of 10deg C is actually 283 deg absolute. If there was a temperature
gradient in the air, the temperature falling fast enough as height
increased, that could in theory be enough to counteract the effects of the
falling pressure. In that case the air-density would conceivably increase,
not decrease, as height increased, which could cause light to be curved
upwards, not downwards; the effect that I think Fred is looking for.

We can try to estimate the temperature gradient that would be needed.

I will work in pounds weight and inches, as I suspect most non-scientists,
and particularly Americans, are happier that way; and will use approximate
values.

At sea level, atmospheric pressure is about 14 pounds to the square inch,
which means that a column of air of 1 square inch area, extending to the
top of the atmosphere (wherever that might be) contains 14 pounds weight of
air.

Now work out the weight of air in just 1 foot height of that column. The
volume is 1/144 cubic foot. At sea level, air has a density of .076 pounds
per cubit foot, so the weight in that small volume is .076/144 pounds or
.00052 pounds. This will reduce the pressure, 1 foot above sea level, by
.00052 pounds per square inch, below its value at sea level which we took
to be 14 pounds per square inch. So by going up a foot above sea level, the
pressure reduces by a fraction  .00052/14, or 1 part in 27,000. If the
temperature were constant the density of air would also reduce, by 1 part
in 27,000 for each foot of elevation.

Now we have to ask what temperature gradient would be needed to null out
that density gradient. The absolute temperature would have to decrease with
altitude by that same factor, 1 part in 27,000, for each foot of rise. At
an ambient temperature of 283 degrees absolute, this would require an air
temperature decrease per foot of elevation of 283/27,000, or .0105 degrees
C per foot, or 1 deg C fall for each 95 feet of height. If the temperature
gradient exceeds this magic figure then light will be bent in the opposite
way to what we would normally expect.

I hope someone will check out the numbers, and the reasoning, in that
passage above, which takes me out of familiar territory.

How likely is that to occur? Very likely, to the extent that we have all
seen it happen! Driving along a road on a still, sunny, day, we are
familiar with what appear to be blue "pools" on the tarmac surface, which
vanish as we approach. What's happening here is that the air just above the
road is strongly heated by the hot road surface, which in turn was heated
by the Sun. Light rays passing through this thin layer above the road see a
strong temperature gradient which causes a reversed bending, so a shallowly
descending ray from the blue sky just skimming the road surface curves into
a rising ray, so the driver sees a reflected image of a bit of the sky,
just where he expects the road to be.

Similar effects cause mirages and can give rise to anomalous dip, at sea.
They can happen particularly when hot air blows from a desert coastline.

Fred, I think, is aware of such local phenomena and asks about the
possibility of light from astronomical or distant earthly objects being
bent in this anomalous way. For that to happen, the temperature gradient
over all, or most of the long light path would have to exceed the value
calculated above. Only a meteorologist could answer that part of the
question, but I will stick my neck out and guess that it's highly unlikely.

George.

================================================================
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.
================================================================

   

Reply