A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Refraction. was: Bubble Horizon Altitude Corrections
From: John Brenneise
Date: 2004 Jul 5, 15:30 -0700
From: John Brenneise
Date: 2004 Jul 5, 15:30 -0700
When speaking of an index of refraction, the usual context is that of explaining the bending of light rays at the boundary between transmission media. In our case, from the near vacuum of interplanetary space (index of refraction = 1.0...) to air (at STP, index of refraction = 1.0003). Snell's law describes the geometry of the bend, where: n1 is the index of refraction in the previous media theta1 is the angle of the ray in the previous media, measured from the normal vector to the plane of interface. n2 is the index of refraction in the new media theta2 is the angle of the ray in the new media, measured from the normal vector to the plane of interface. n1*sin(theta1) = n2*sin(theta2) As the density of the atmosphere increases with decreasing altitude the index of refraction increases. Whenever the index of refraction increases in the transition from the old media to the new media, the ray will bend toward the normal vector to the plane of the interface, making the angle of elevation grow. So, a decrease in the angle of elevation would require a decrease in the index of refraction. A decrease in the index of refraction would require an atmospheric event that produces a harder vacuum than interplanetary space. This seems awfully unlikely to me. John ----- Original Message ----- From: "George Huxtable"
To: Sent: Monday, July 05, 2004 2:44 PM Subject: Refraction. was: Bubble Horizon Altitude Corrections > 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 email@example.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. > ================================================================